Mathematics

Research

10 pages, 261 KiB

Open AccessArticle

Properties for Close-to-Convex and Quasi-Convex Functions Using q-Linear Operator

by Ekram E. Ali, Rabha M. El-Ashwah, Abeer M. Albalahi and Wael W. Mohammed

Mathematics 2025, 13(6), 900; https://doi.org/10.3390/math13060900 - 7 Mar 2025

Viewed by 235

Abstract

In this work, we describe the

q

-analogue of a multiplier–Ruscheweyh operator of a specific family of linear operators

I_{q, ρ}^{s} (ν, τ)

, and we obtain findings related to geometric function theory (GFT) by utilizing approaches [...] Read more.

In this work, we describe the

q

-analogue of a multiplier–Ruscheweyh operator of a specific family of linear operators

I_{q, ρ}^{s} (ν, τ)

, and we obtain findings related to geometric function theory (GFT) by utilizing approaches established through subordination and knowledge of

q

-calculus operators. By using this operator, we develop generalized classes of quasi-convex and close-to-convex functions in this paper. Additionally, the classes

K_{q, ρ}^{s} (ν, τ) (φ)

,

Q_{q, ρ}^{s} (ν, τ) (φ)

are introduced. The invariance of these recently formed classes under the

q

-Bernardi integral operator is investigated, along with a number of intriguing inclusion relationships between them. Additionally, several unique situations and the beneficial outcomes of these studies are taken into account. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

30 pages, 384 KiB

Open AccessArticle

Radius of α-Spirallikeness of Order cos(α)/2 for Entire Functions

by Narjes Alabkary and Saiful R. Mondal

Mathematics 2025, 13(5), 796; https://doi.org/10.3390/math13050796 - 27 Feb 2025

Viewed by 391

Abstract

We determine the radius of

α

-spirallikeness of order

\cos (α) / 2

for entire functions represented as infinite products of their positive zeros. The discussion includes several examples featuring special functions such as Gamma functions, Bessel functions, Struve functions, Wright [...] Read more.

We determine the radius of

α

-spirallikeness of order

\cos (α) / 2

for entire functions represented as infinite products of their positive zeros. The discussion includes several examples featuring special functions such as Gamma functions, Bessel functions, Struve functions, Wright functions, Ramanujan-type entire functions, and q-Bessel functions. We also consider combinations of classical Bessel functions, including both first-order and second-order derivatives. Additionally, several other special functions that can be incorporated into the established classes are described. We utilize Mathematica 12 software to compute the numerical values of the radius for some functions. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

12 pages, 376 KiB

Open AccessArticle

Toeplitz Determinants for Inverse of Analytic Functions

by Sarem H. Hadi, Yahea Hashem Saleem, Alina Alb Lupaş, Khalid M. K. Alshammari and Abdullah Alatawi

Mathematics 2025, 13(4), 676; https://doi.org/10.3390/math13040676 - 19 Feb 2025

Viewed by 239

Abstract

Estimates bounds for Carathéodory functions in the complex domain are applied to demonstrate sharp limits for the inverse of analytic functions. Determining these values is considered a more difficult task compared to finding the values of analytic functions themselves. The challenge lies in [...] Read more.

Estimates bounds for Carathéodory functions in the complex domain are applied to demonstrate sharp limits for the inverse of analytic functions. Determining these values is considered a more difficult task compared to finding the values of analytic functions themselves. The challenge lies in finding the sharp estimate for the functionals. While some recent studies have made progress in calculating the sharp boundary values of Hankel determinants associated with inverse functions, the Toeplitz determinant is yet to be addressed. Our research aims to estimate the determinants of the Toeplitz matrix, which is also linked to inverse functions. We also focus on computing these determinants for familiar analytical functions (pre-starlike, starlike, convex, symmetric-starlike) while investigating coefficient values. The study also provides an improvement to the estimation of the determinants of the pre-starlike class presented by Li and Gou. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

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12 pages, 250 KiB

Open AccessArticle

On a New Class of Concave Bi-Univalent Functions Associated with Bounded Boundary Rotation

by Prathviraj Sharma, Srikandan Sivasubramanian, Gangadharan Murugusundaramoorthy and Nak Eun Cho

Mathematics 2025, 13(3), 370; https://doi.org/10.3390/math13030370 - 23 Jan 2025

Viewed by 624

Abstract

In this research article, we introduce a new subclass of concave bi-univalent functions associated with bounded boundary rotation defined on an open unit disk. For this new class, we make an attempt to find the first two initial coefficient bounds. In addition, we [...] Read more.

In this research article, we introduce a new subclass of concave bi-univalent functions associated with bounded boundary rotation defined on an open unit disk. For this new class, we make an attempt to find the first two initial coefficient bounds. In addition, we investigate the very famous Fekete–Szegö inequality for functions belonging to this new subclass of concave bi-univalent functions related to bounded boundary rotation. For some particular choices of parameters, we derive the earlier estimates on the coefficient bounds, which are stated at the end. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

17 pages, 364 KiB

Open AccessArticle

Two Families of Bi-Univalent Functions Associating the (p, q)-Derivative with Generalized Bivariate Fibonacci Polynomials

by Sondekola Rudra Swamy, Basem Aref Frasin, Daniel Breaz and Luminita-Ioana Cotîrlă

Mathematics 2024, 12(24), 3933; https://doi.org/10.3390/math12243933 - 13 Dec 2024

Cited by 1 | Viewed by 669

Abstract

Making use of generalized bivariate Fibonacci polynomials, we propose two families of regular functions of the type

ϕ (ζ) = ζ + \sum_{j = 2}^{\infty} d_{j} ζ^{j}

, which are bi-univalent in the disc [...] Read more.

Making use of generalized bivariate Fibonacci polynomials, we propose two families of regular functions of the type

ϕ (ζ) = ζ + \sum_{j = 2}^{\infty} d_{j} ζ^{j}

, which are bi-univalent in the disc

{ζ \in C : | ζ | < 1}

involving the (p, q)-derivative operator. We find estimates on the coefficients

| d_{2} |

,

| d_{3} |

and the of Fekete–Szegö functional for members of these families. Relevant connections to the existing results and new consequences of the main result are presented. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

14 pages, 293 KiB

Open AccessArticle

Fuzzy Subordination Results for Meromorphic Functions Associated with Hurwitz–Lerch Zeta Function

by Ekram E. Ali, Georgia Irina Oros, Rabha M. El-Ashwah, Abeer M. Albalahi and Marwa Ennaceur

Mathematics 2024, 12(23), 3721; https://doi.org/10.3390/math12233721 - 27 Nov 2024

Viewed by 682

Abstract

The notion of the fuzzy set was incorporated into geometric function theory in recent years, leading to the emergence of fuzzy differential subordination theory, which is a generalization of the classical differential subordination notion. This article employs a new integral operator introduced using [...] Read more.

The notion of the fuzzy set was incorporated into geometric function theory in recent years, leading to the emergence of fuzzy differential subordination theory, which is a generalization of the classical differential subordination notion. This article employs a new integral operator introduced using the class of meromorphic functions, the notion of convolution, and the Hurwitz–Lerch Zeta function for obtaining new fuzzy differential subordination results. Furthermore, the best fuzzy dominants are provided for each of the fuzzy differential subordinations investigated. The results presented enhance the approach to fuzzy differential subordination theory by giving new results involving operators in the study, for which starlikeness and convexity properties are revealed using the fuzzy differential subordination theory. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

12 pages, 273 KiB

Open AccessArticle

Introducing the Third-Order Fuzzy Superordination Concept and Related Results

by Georgia Irina Oros, Simona Dzitac and Daniela Andrada Bardac-Vlada

Mathematics 2024, 12(19), 3095; https://doi.org/10.3390/math12193095 - 2 Oct 2024

Cited by 2 | Viewed by 911

Abstract

Third-order fuzzy differential subordination studies were recently initiated by developing the main concepts necessary for obtaining new results on this topic. The present paper introduces the dual concept of third-order fuzzy differential superordination by building on the known results that are valid for [...] Read more.

Third-order fuzzy differential subordination studies were recently initiated by developing the main concepts necessary for obtaining new results on this topic. The present paper introduces the dual concept of third-order fuzzy differential superordination by building on the known results that are valid for second-order fuzzy differential superordination. The outcome of this study offers necessary and sufficient conditions for determining subordinants of a third-order fuzzy differential superordination and, furthermore, for finding the best subordinant for such fuzzy differential superordiantion, when it can be obtained. An example to suggest further uses of the new outcome reported in this work is enclosed to conclude this study. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

11 pages, 252 KiB

Open AccessArticle

Applications of Generalized Hypergeometric Distribution on Comprehensive Families of Analytic Functions

by Tariq Al-Hawary, Basem Frasin and Ibtisam Aldawish

Mathematics 2024, 12(18), 2851; https://doi.org/10.3390/math12182851 - 13 Sep 2024

Viewed by 1081

Abstract

A sequence of n trials from a finite population with no replacement is described by the hypergeometric distribution as the number of successes. Calculating the likelihood that factory-produced items would be defective is one of the most popular uses of the hypergeometric distribution [...] Read more.

A sequence of n trials from a finite population with no replacement is described by the hypergeometric distribution as the number of successes. Calculating the likelihood that factory-produced items would be defective is one of the most popular uses of the hypergeometric distribution in industrial quality control. Very recently, several researchers have applied this distribution on certain families of analytic functions. In this study, we provide certain adequate criteria for the generalized hypergeometric distribution series to be in two families of analytic functions defined in the open unit disk. Furthermore, we consider an integral operator for the hypergeometric distribution. Some corollaries will be implied from our main results. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

14 pages, 296 KiB

Open AccessArticle

Sufficiency Conditions for a Class of Convex Functions Connected with Tangent Functions Associated with the Combination of Babalola Operators and Binomial Series

by Sheza M. El-Deeb and Luminita-Ioana Cotîrlă

Mathematics 2024, 12(11), 1691; https://doi.org/10.3390/math12111691 - 29 May 2024

Cited by 1 | Viewed by 602

Abstract

In this paper, we create a new subclass of convex functions given with tangent functions applying the combination of Babalola operators and Binomial series. Moreover, we obtain several important geometric results, including sharp coefficient bounds, sharp Fekete–Szego inequality, Kruskal inequality, and growth and [...] Read more.

In this paper, we create a new subclass of convex functions given with tangent functions applying the combination of Babalola operators and Binomial series. Moreover, we obtain several important geometric results, including sharp coefficient bounds, sharp Fekete–Szego inequality, Kruskal inequality, and growth and distortion estimates. Furthermore, for functions with logarithmic coefficients, we compute sharp Fekete–Szego inequality and sharp coefficient bounds. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

15 pages, 659 KiB

Open AccessArticle

A Class of Bi-Univalent Functions in a Leaf-Like Domain Defined through Subordination via

q ̧

-Calculus

by Abdullah Alsoboh and Georgia Irina Oros

Mathematics 2024, 12(10), 1594; https://doi.org/10.3390/math12101594 - 20 May 2024

Cited by 6 | Viewed by 1148

Abstract

Bi-univalent functions associated with the leaf-like domain within open unit disks are investigated, and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with

q

-calculus. The [...] Read more.

Bi-univalent functions associated with the leaf-like domain within open unit disks are investigated, and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with

q

-calculus. The class is proved to not be empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on

| α_{2} |

and

| α_{3} |

coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

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13 pages, 250 KiB

Open AccessArticle

Bridging the p-Special Functions between the Generalized Hyperbolic and Trigonometric Families

by Ali Hamzah Alibrahim and Saptarshi Das

Mathematics 2024, 12(8), 1242; https://doi.org/10.3390/math12081242 - 19 Apr 2024

Cited by 1 | Viewed by 1499

Abstract

Here, we study the extension of p-trigonometric functions

sinp

and

cosp

family in complex domains and p-hyperbolic functions

sinhp

and the

coshp

family in hyperbolic complex domains. These functions satisfy analogous relations as their classical counterparts with some unknown properties. We [...] Read more.

Here, we study the extension of p-trigonometric functions

sinp

and

cosp

family in complex domains and p-hyperbolic functions

sinhp

and the

coshp

family in hyperbolic complex domains. These functions satisfy analogous relations as their classical counterparts with some unknown properties. We show the relationship of these two classes of special functions viz. p-trigonometric and p-hyperbolic functions with imaginary arguments. We also show many properties and identities related to the analogy between these two groups of functions. Further, we extend the research bridging the concepts of hyperbolic and elliptical complex numbers to show the properties of logarithmic functions with complex arguments. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

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