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Keywords = subordination and superordination

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19 pages, 278 KB  
Article
“The Only People That Really Understand”: A Qualitative Study of Healthcare Workers’ COVID-19 Experiences and Implications for Workplace Support
by Brian En Chyi Lee, Elizabeth M. Clancy, Leanne Boyd, Andrea Reupert, Nicholas F. Taylor, Sherrica Senewiratne and Jade Sheen
Healthcare 2026, 14(10), 1400; https://doi.org/10.3390/healthcare14101400 - 20 May 2026
Viewed by 199
Abstract
Background: Healthcare systems globally continue to experience persistent workforce and system-level challenges as increased workloads, lasting wellbeing impacts, and retention issues remain following the pandemic. To inform strategies and interventions to address these issues, this paper explored the workplace experiences of Victorian [...] Read more.
Background: Healthcare systems globally continue to experience persistent workforce and system-level challenges as increased workloads, lasting wellbeing impacts, and retention issues remain following the pandemic. To inform strategies and interventions to address these issues, this paper explored the workplace experiences of Victorian (Australia) frontline healthcare workers with parenting responsibilities during the COVID-19 pandemic. Methods: A total of 39 frontline healthcare workers from a large metropolitan hospital were interviewed between October 2020 and February 2021. Reflexive thematic analysis was used to analyse transcripts. Results: Three superordinate themes and five subordinate themes were identified. Themes highlighted the significant pressure that rapid workplace changes placed on healthcare staff and leaders, affecting their physical, mental, and relational health. Support from peers and supervisors was protective, though this increased demands on supervisors themselves. While many staff reported pride in their work, some experienced reduced career satisfaction and concerns about lasting psychological impacts. Conclusions: This study identifies how workplace supports operate through communication transparency, leadership capacity, and protected peer-support space, translating to organisational priorities for the post-pandemic workforce. In the context of ongoing workforce shortages and heightened demands post-pandemic, these findings underscore the importance of strengthening leadership capacity, embedding sustainable workplace supports, and addressing the psychological needs of healthcare staff. Such system-level responses are essential for pandemic recovery, improving workforce retention and staff wellbeing in the modern healthcare environment. Full article
(This article belongs to the Special Issue Work Conditions and Mental Health in Healthcare Workers)
24 pages, 377 KB  
Article
Third-Order Fuzzy Differential Subordination and Superordination via Generalized Mittag-Leffler Operator with Applications in Decision Making
by Borhen Halouani, Bushra Kanwal, Saba Shabir, Maslina Darus, Tariq Alsmadi and Ibrahim S. Elshazly
Mathematics 2026, 14(8), 1310; https://doi.org/10.3390/math14081310 - 14 Apr 2026
Viewed by 289
Abstract
This article focuses on the notions of third-order fuzzy differential subordination and superordination associated with the generalized Mittag-Leffler operator. Methods emphasizing the key concept of admissible functions are implemented to investigate several third-order fuzzy differential subordination and superordination results. Sandwich-type outcomes are established [...] Read more.
This article focuses on the notions of third-order fuzzy differential subordination and superordination associated with the generalized Mittag-Leffler operator. Methods emphasizing the key concept of admissible functions are implemented to investigate several third-order fuzzy differential subordination and superordination results. Sandwich-type outcomes are established based on the adopted methodology, linking the dual fuzzy theoretical frameworks. In addition, the applications of fuzzy differential subordination are discussed in the context of decision making problems. The proposed approach provides the mathematical mechanism that ensures the stability and preservation of the decision under changes in criteria and preference evaluations, highlighting the importance of the developed theory. Full article
(This article belongs to the Section C: Mathematical Analysis)
15 pages, 1087 KB  
Article
Third-Order Differential Subordination for Analytic Functions Involving the Lommel Function of the First Kind
by Suha Hammad, Mohammad El-Ityan, Tariq Al-Hawary, Ibtisam Aldawish and Feras Yousef
Symmetry 2026, 18(4), 642; https://doi.org/10.3390/sym18040642 - 10 Apr 2026
Viewed by 451
Abstract
This study investigates third-order differential subordination and its influence on classes of analytic functions associated with the Lommel function of the first kind. By employing a newly defined operator Lwjf(z), we identify and characterize the admissible [...] Read more.
This study investigates third-order differential subordination and its influence on classes of analytic functions associated with the Lommel function of the first kind. By employing a newly defined operator Lwjf(z), we identify and characterize the admissible function classes that satisfy the corresponding third-order differential subordinations. These admissibility conditions enable the derivation of several key results, including a sandwich-type theorem obtained as a direct consequence of the established framework. The findings contribute to a broader understanding of analytic functions governed by higher-order differential constraints and highlight the significant role played by the Lommel function in shaping these geometric properties. Full article
(This article belongs to the Special Issue Mathematics: Feature Papers 2026)
13 pages, 290 KB  
Article
Fuzzy Study Regarding the Fractional Integral Applied to the q-Multiplier Transformation
by Alina Alb Lupaş and Daria Lupaş
Symmetry 2026, 18(4), 549; https://doi.org/10.3390/sym18040549 - 24 Mar 2026
Viewed by 263
Abstract
q-calculus and fractional calculus combined with geometric function theory lead to remarkable results. The fractional integral introduced by Riemann–Liouville applied to the q-multiplier transformation is used in this research to study the two dual theories of fuzzy differential subordination and fuzzy [...] Read more.
q-calculus and fractional calculus combined with geometric function theory lead to remarkable results. The fractional integral introduced by Riemann–Liouville applied to the q-multiplier transformation is used in this research to study the two dual theories of fuzzy differential subordination and fuzzy differential superordination and to develop specific fuzzy results. In the theorems examining fuzzy differential subordinations and fuzzy differential superordinations, fuzzy best dominants and fuzzy best subordinants are also provided. In addition, the demonstrated outcomes reveal corollaries by taking specific functions with established geometric features into consideration as the fuzzy best subordinant and fuzzy best dominant. The work concludes with a fuzzy differential sandwich theorem and related corollaries that combine the findings of this research on fuzzy differential subordinations and superordinations. Full article
(This article belongs to the Special Issue Symmetry and Fuzzy Set)
15 pages, 259 KB  
Article
The Lived Experience of Couples Undergoing In Vitro Fertilisation in Greece: An Interpretative Phenomenological Analysis
by George Koulierakis, Apostolia-Konstantina Theodosiou, Eleftheria Karampli and Angeliki Liarigkovinou
Healthcare 2026, 14(6), 802; https://doi.org/10.3390/healthcare14060802 - 21 Mar 2026
Viewed by 852
Abstract
Background/Objectives: Research examining the emotional and psychological challenges experienced by couples undergoing in vitro fertilisation (IVF) remains limited. Existing evidence suggests that women undergoing IVF often report elevated levels of depression, anxiety, and emotional distress, whereas men may experience feelings of anger, [...] Read more.
Background/Objectives: Research examining the emotional and psychological challenges experienced by couples undergoing in vitro fertilisation (IVF) remains limited. Existing evidence suggests that women undergoing IVF often report elevated levels of depression, anxiety, and emotional distress, whereas men may experience feelings of anger, inadequacy, and self-doubt, especially following unsuccessful treatment cycles. Successful IVF outcomes are commonly associated with intense joy, relief, and fulfilment as couples realise their aspiration to become parents. In light of the limited qualitative research conducted in Greece to date, in the present study, we aimed to explore the lived experiences of couples undergoing IVF treatment, with particular attention to emotional, relational, and systemic dimensions. Methods: A qualitative research design was employed. Semi-structured, in-depth interviews were conducted with six heterosexual couples (aged 18–49 years) residing in Athens and Karditsa, Greece, all of whom had undergone IVF treatment. Interviews were audio-recorded, transcribed verbatim, and analysed using Interpretative Phenomenological Analysis. Results: Our analysis revealed five interrelated superordinate themes with associated subordinate themes: (1) making sense of infertility and IVF, (2) negotiating relationships under the strain of IVF, (3) IVF as an emotionally demanding journey, (4) navigating institutional and systemic barriers, and (5) projecting the future through IVF experience. Lived experiences of infertile couples undergoing IVF treatment highlighted a range of emotions, social pressure, and attitudes towards IVF and related policies. Conclusions: In Greece, where demographic decline has been widely discussed in policy debates, IVF has gained societal and policy attention. For many participants, IVF represented a hopeful pathway towards achieving parenthood despite the emotional and practical challenges involved. Full article
21 pages, 365 KB  
Article
Sandwich Results for Holomorphic Functions Related to an Integral Operator
by Amal Mohammed Darweesh, Adel Salim Tayyah, Sarem H. Hadi and Alina Alb Lupaş
Fractal Fract. 2026, 10(3), 171; https://doi.org/10.3390/fractalfract10030171 - 4 Mar 2026
Cited by 2 | Viewed by 326
Abstract
In this paper, we introduce a new logarithmic integral operator that unifies differentiation and fractional integration within the complex domain. The present work addresses this gap by applying the proposed operator to analytic functions represented by alternating power series. The method demonstrates that [...] Read more.
In this paper, we introduce a new logarithmic integral operator that unifies differentiation and fractional integration within the complex domain. The present work addresses this gap by applying the proposed operator to analytic functions represented by alternating power series. The method demonstrates that the coefficients can be reorganized in a controlled manner without affecting convergence or analytic behavior. Using this framework, we derive third-order differential subordination and superordination results, which naturally lead to corresponding sandwich-type results. The findings confirm that the introduced operator offers an effective analytical tool for studying distortion, growth, and mapping properties of analytic functions, with promising potential for future applications in fluid mechanics. Full article
28 pages, 400 KB  
Article
New Certain Results of a Linear Multiplier Fractional q-Differintegral Operator for Fuzzy Differential Subordination and Superordination
by Ningegwoda Ravikumar, Basem Aref Frasin, Rmsen Abdulbari Ali Ahmed and Ibtisam Aldawish
Fractal Fract. 2026, 10(3), 170; https://doi.org/10.3390/fractalfract10030170 - 4 Mar 2026
Viewed by 373
Abstract
The concept of fuzzy differential subordination was introduced in 2011 as a natural generalization of classical differential subordination, reflecting the contemporary trend of incorporating fuzzy set theory into well-established mathematical frameworks. This work aims to explore multiple fuzzy differential subordinations (FDS) and fuzzy [...] Read more.
The concept of fuzzy differential subordination was introduced in 2011 as a natural generalization of classical differential subordination, reflecting the contemporary trend of incorporating fuzzy set theory into well-established mathematical frameworks. This work aims to explore multiple fuzzy differential subordinations (FDS) and fuzzy differential superordinations (FDSs) associated with the linear multiplier fractional q-differintegral operator. Utilizing the linear multiplier fractional q-differintegral operator, we introduce a novel fuzzy subclass of analytic functions, denoted by SDFσ,m(q,λ,γ). Using the concept of FDS and FDSs, we identify important characteristics and analytical aspects of the class SDFσ,m(q,λ,γ). Furthermore, we derive a collection of FDS and FDSs results specifically related to the linear multiplier fractional q-differintegral operator. Full article
19 pages, 532 KB  
Article
Third-Order Fuzzy Differential Results for Meromorphic Functions Using a Linear Operator: Subordination and Superordination
by Mays S. Abdul Ameer, Abdul Rahman S. Juma and Hassan Hussien Ebrahim
Symmetry 2026, 18(3), 413; https://doi.org/10.3390/sym18030413 - 27 Feb 2026
Viewed by 240
Abstract
While over a hundred articles discuss second-order differential inequalities and subordinations in the complex plane, very few address the relatively unexplored classes of third-order fuzzy differential subordination and superordination. This paper builds upon the recently proposed concepts of third-order fuzzy differential subordination and [...] Read more.
While over a hundred articles discuss second-order differential inequalities and subordinations in the complex plane, very few address the relatively unexplored classes of third-order fuzzy differential subordination and superordination. This paper builds upon the recently proposed concepts of third-order fuzzy differential subordination and superordination, which are developed using a linear operator and a meromorphic function. By applying techniques based on the fundamental notion of admissible functions, we begin by defining the appropriate class of such functions necessary for deriving new results in third-order fuzzy differential subordination. The study reveals the establishment of sandwich-type theorems, linking these new findings with established methods in third-order fuzzy differentiation and superordination theory. Full article
(This article belongs to the Section Mathematics)
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23 pages, 345 KB  
Article
On Certain Subclasses of Analytic Functions Associated with a Symmetric q-Differential Operator
by Vasile-Aurel Caus
Mathematics 2025, 13(17), 2860; https://doi.org/10.3390/math13172860 - 4 Sep 2025
Cited by 2 | Viewed by 1174
Abstract
This paper explores a class of analytic functions defined in the open unit disk by means of a symmetric q-differential operator. In the first part, we derive sufficient conditions for functions to belong to a subclass associated with this operator, using inequalities [...] Read more.
This paper explores a class of analytic functions defined in the open unit disk by means of a symmetric q-differential operator. In the first part, we derive sufficient conditions for functions to belong to a subclass associated with this operator, using inequalities involving their coefficients. Additionally, we establish several inclusion relations between these subclasses, obtained by varying the defining parameters. In the second part, we focus on differential subordination and superordination for functions transformed by the operator. We provide sufficient conditions under which such functions are subordinate or superordinate to univalent functions, and we determine the best dominant and best subordinant in specific cases. These results are complemented by several corollaries that highlight particular instances of the main theorems. Furthermore, we present a sandwich-type result that brings together the subordination and superordination frameworks in a unified analytic statement. Full article
(This article belongs to the Special Issue Current Topics in Geometric Function Theory, 2nd Edition)
19 pages, 322 KB  
Article
Application on Fuzzy Third-Order Subordination and Superordination Connected with Lommel Function
by Ekram E. Ali, Georgia Irina Oros, Rabha M. El-Ashwah and Abeer M. Albalahi
Mathematics 2025, 13(12), 1917; https://doi.org/10.3390/math13121917 - 8 Jun 2025
Cited by 3 | Viewed by 708
Abstract
This work is based on the recently introduced concepts of third-order fuzzy differential subordination and its dual, third-order fuzzy differential superordination. In order to obtain the new results that add to the development of the newly initiated lines of research, a new operator [...] Read more.
This work is based on the recently introduced concepts of third-order fuzzy differential subordination and its dual, third-order fuzzy differential superordination. In order to obtain the new results that add to the development of the newly initiated lines of research, a new operator is defined here using the concept of convolution and the normalized Lommel function. The methods focusing on the basic concept of admissible function are employed. Hence, the investigation of new third-order fuzzy differential subordination results starts with the definition of the suitable class of admissible functions. The first theorems discuss third-order fuzzy differential subordinations involving the newly introduced operator. The following result shows the conditions needed such that the fuzzy best dominant can be found for a third-order fuzzy differential subordination. Next, dual results are obtained by employing the methods of third-order fuzzy differential superordination based on the same concept of an admissible function. A suitable class of admissible functions is introduced and new third-order fuzzy differential superordinations are obtained, showing how the best subordinant can be obtained under certain restrictions. As a conclusion of this study, sandwhich-type results are derived, linking the outcome of the two dual fuzzy theories. Full article
(This article belongs to the Special Issue Current Topics in Geometric Function Theory, 2nd Edition)
23 pages, 340 KB  
Article
Third-Order Fuzzy Subordination and Superordination on Analytic Functions on Punctured Unit Disk
by Ekram E. Ali, Georgia Irina Oros, Rabha M. El-Ashwah and Abeer M. Albalahi
Axioms 2025, 14(5), 378; https://doi.org/10.3390/axioms14050378 - 17 May 2025
Cited by 1 | Viewed by 659
Abstract
This work’s theorems and corollaries present new third-order fuzzy differential subordination and superordination results developed by using a novel convolution linear operator involving the Gaussian hypergeometric function and a previously studied operator. The paper reveals methods for finding the best dominant and best [...] Read more.
This work’s theorems and corollaries present new third-order fuzzy differential subordination and superordination results developed by using a novel convolution linear operator involving the Gaussian hypergeometric function and a previously studied operator. The paper reveals methods for finding the best dominant and best subordinant for the third-order fuzzy differential subordinations and superordinations, respectively. The investigation concludes with the assertion of sandwich-type theorems connecting the conclusions of the studies conducted using the particular methods of the theories of the third-order fuzzy differential subordination and superordination, respectively. Full article
(This article belongs to the Special Issue Advances in Geometric Function Theory and Related Topics)
39 pages, 480 KB  
Article
Exploring the Role of Psychedelic Experiences on Wellbeing and Symptoms of Disordered Eating
by Nadine Loh and David Luke
Psychoactives 2025, 4(1), 7; https://doi.org/10.3390/psychoactives4010007 - 4 Mar 2025
Cited by 1 | Viewed by 7540
Abstract
Accumulating psychedelic research has demonstrated a potential for improving mental health and wellbeing, yet studies in the context of eating disorders (EDs) are limited. This study aims to explore the subjective effects of psychedelic experiences to gain insight into the benefits and risks [...] Read more.
Accumulating psychedelic research has demonstrated a potential for improving mental health and wellbeing, yet studies in the context of eating disorders (EDs) are limited. This study aims to explore the subjective effects of psychedelic experiences to gain insight into the benefits and risks for people with EDs. Semi-structured interviews were conducted with eight adults aged 25–54 (mean age = 36.9), reporting to have had experiences with EDs and psychedelics in both naturalistic and clinical settings. Participants had multiple diagnoses and suffered chronic EDs, (mean age of onset = 13), diagnosed (N = 7) and undiagnosed (N = 1). Reports of cessation or the reduction of ED symptoms were unanimous and long-lasting for seven, with two participants reporting recovery attributed to psychedelic use. Two participants reported relapsing, attributed to environmental factors in the months following. Thematic analysis resulted in two superordinate themes, each comprising three subordinate themes. The first superordinate theme, ‘Exploring’ via the ‘gateway to healing’, illustrates mental, emotional, and transcendental elements of psychedelic experiences. The second superordinate theme, ‘Transformation’ and being ‘able to do the work’, illustrates cognitive and behavioural outcomes, with retrospective safety perceptions. These findings may provide more in-depth information on what benefits and experiences people with EDs can obtain from the use of psychedelic drugs and may inform more robust investigations of psychedelic-assisted therapy for the treatment of EDs. Full article
(This article belongs to the Special Issue Natural Hallucinogens in Mental Health)
18 pages, 288 KB  
Article
Application of Fuzzy Subordinations and Superordinations for an Analytic Function Connected with q-Difference Operator
by Ekram E. Ali, Rabha M. El-Ashwah and Abeer M. Albalahi
Axioms 2025, 14(2), 138; https://doi.org/10.3390/axioms14020138 - 15 Feb 2025
Cited by 1 | Viewed by 880
Abstract
This paper extends the idea of subordination from the theory of fuzzy sets to the geometry theory of analytic functions with a single complex variable. The purpose of this work is to define fuzzy subordination and illustrate its main characteristics. New fuzzy differential [...] Read more.
This paper extends the idea of subordination from the theory of fuzzy sets to the geometry theory of analytic functions with a single complex variable. The purpose of this work is to define fuzzy subordination and illustrate its main characteristics. New fuzzy differential subordinations will be introduced with the help of this effort. We define a linear operator Iq,ρs(ν,ς) using the concept of the q-calculus operators. New fuzzy differential subordinations are created by employing the previously described operator, functions from the new class, and well-known lemmas. Specific corollaries derived from the operator proved the many examples created for the fuzzy differential subordinations, as well as the theorems, and demonstrate how the new theoretical conclusions apply to the fuzzy differential superordinations provided in this research. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory, 3rd Edition)
19 pages, 294 KB  
Article
Quantum–Fractal–Fractional Operator in a Complex Domain
by Adel A. Attiya, Rabha W. Ibrahim, Ali H. Hakami, Nak Eun Cho and Mansour F. Yassen
Axioms 2025, 14(1), 57; https://doi.org/10.3390/axioms14010057 - 13 Jan 2025
Cited by 6 | Viewed by 1932
Abstract
In this effort, we extend the fractal–fractional operators into the complex plane together with the quantum calculus derivative to obtain a quantum–fractal–fractional operators (QFFOs). Using this newly created operator, we create an entirely novel subclass of analytical functions in the unit disk. Motivated [...] Read more.
In this effort, we extend the fractal–fractional operators into the complex plane together with the quantum calculus derivative to obtain a quantum–fractal–fractional operators (QFFOs). Using this newly created operator, we create an entirely novel subclass of analytical functions in the unit disk. Motivated by the concept of differential subordination, we explore the most important geometric properties of this novel operator. This leads to a study on a set of differential inequalities in the open unit disk. We focus on the conditions to obtain a bounded turning function of QFFOs. Some examples are considered, involving special functions like Bessel and generalized hypergeometric functions. Full article
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)
16 pages, 352 KB  
Article
Sandwich-Type Results and Existence Results of Analytic Functions Associated with the Fractional q-Calculus Operator
by Sudhansu Palei, Madan Mohan Soren, Daniel Breaz and Luminiţa-Ioana Cotîrlǎ
Fractal Fract. 2025, 9(1), 4; https://doi.org/10.3390/fractalfract9010004 - 25 Dec 2024
Cited by 2 | Viewed by 1038
Abstract
In the present investigation, we present certain subordination and superordination results for the q-integral operator of a fractional order associated with analytic functions in the open unit disk U. Using this q-integral operator, we obtain sandwich-type results. Furthermore, we employ [...] Read more.
In the present investigation, we present certain subordination and superordination results for the q-integral operator of a fractional order associated with analytic functions in the open unit disk U. Using this q-integral operator, we obtain sandwich-type results. Furthermore, we employ the existence of univalent solutions to a q-differential equation connected with a fractional q-integral operator of fractional order. We use these results to demonstrate the significance of our findings for particular functions. We also derive some examples and corollaries that are pertinent to our results. Full article
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