Search Results (33)

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 study presents the soft limit and upper (lower) soft limit proposed by Molodtsov, with several theoretical contributions. It investigates some of their basic properties, such as some fundamental soft limit rules, the relation between soft limit and boundedness, and the sandwich/squeeze theorem. Moreover, the paper proposes left and right soft limits and studies some of their main properties. Furthermore, it defines the soft limit at infinity and explores some of its basic properties. Additionally, the present study exemplifies these concepts and their properties to better understand them. The paper then compares the aforesaid concepts with their classical forms. Afterward, this paper presents soft continuity and upper (lower) soft continuity, proposed by Molodtsov, theoretically contributes to these concepts, and investigates some of their key properties, such as some fundamental soft continuity rules, the relation between soft continuity and boundedness, Bolzano’s theorem, and the intermediate value theorem. Moreover, it defines left and right soft continuity and studies some of their basic properties. The present study exemplifies soft continuity types and their properties. In addition, it compares them with their classical forms. Finally, this study discusses whether the aspects should be further analyzed. Full article

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 study is concerned with the class of p-valent meromorphic functions, represented by the series $f\left(\zeta \right)={\zeta }^{-p}+{\sum }_{k=1-p}^{\infty }{d}_k{\zeta }^k$, with the domain characterized by $0<\left|\zeta \right|<1$. We apply an Erdelyi–Kober-type integral operator to derive two recurrence relations. From this, we draw specific conclusions on differential subordination and differential superordination. By looking into suitable classes of permitted functions, we obtain various outcomes, including results analogous to sandwich-type theorems. The operator used can provide generalizations of previous operators through specific parameter choices, thus providing more corollaries. Full article

In this paper, we aim to give some results for third-order differential subordination for analytic functions in the open unit disk $\mathcal{U}=\left\{z:z\in \mathbb{C} \mathrm{a}\mathrm{n}\mathrm{d} \left|z\right|<1\right\}$ involving the new integral operator ${\mu }_{\alpha ,n}^m(f\ast g)$. The results are obtained by examining pertinent classes of acceptable functions. New findings on differential subordination have been obtained. Additionally, some specific cases are documented. This work investigates appropriate classes of admissible functions, presents a novel of new integral operator, and discusses the properties of third-order differential subordination. The properties and results of the differential subordination are symmetrical to the properties of the differential superordination to form the sandwich theorems. Full article

This article aims to significantly advance geometric function theory by providing a valuable contribution to analytic and multivalent functions. It focuses on differential subordination and superordination, which characterize the interactions between analytic functions. To achieve our goal, we employ a method that relies on the characteristics of differential subordination and superordination. As one of the latest advancements in this field, this technique is able to derive several results about differential subordination and superordination for multivalent functions defined by the new operator ${\mathcal{M}}_{\lambda ,p}^m\left(v,\rho ;\eta \right)\mathcal{F}\left(\xi \right)$ within the open unit disk $\mathfrak{A}$. Additionally, by employing the technique, the differential sandwich outcome is achieved. Therefore, this work presents crucial exceptional instances that follow the results. The findings of this paper can be applied to a wide range of mathematical and engineering problems, including system identification, orthogonal polynomials, fluid dynamics, signal processing, antenna technology, and approximation theory. Furthermore, this work significantly advances the knowledge and understanding of the analytical functions of the unit and its interactive higher relations. The characteristics and consequences of differential subordination theory are symmetric to those of differential superordination theory. By combining them, sandwich-type theorems can be derived. Full article

Let ${\left\{X_n\right\}}_{n\in \mathbb{Z}}$ be a stationary process with values in a finite set. In this paper, we present a moving average version of the Shannon–McMillan–Breiman theorem; this generalize the corresponding classical results. A sandwich argument reduced the proof to direct applications of the moving strong law of large numbers. The result generalizes the work by Algoet et. al., while relying on a similar sandwich method. It is worth noting that, in some kind of significance, the indices $a_n$ and $\varphi \left(n\right)$ are symmetrical, i.e., for any integer n, if the growth rate of ${\left(a_n\right)}_{n\in \mathbb{Z}}$ is slow enough, all conclusions in this article still hold true. Full article

This work presents a novel investigation that utilizes the integral operator $I_{p,\lambda }^n$ in the field of geometric function theory, with a specific focus on sandwich theorems. We obtained findings about the differential subordination and superordination of a novel formula for a generalized integral operator. Additionally, certain sandwich theorems were discovered. Full article

The aim of this paper is to introduce a new type of two-dimensional convexity by using total-order relations. In the first part of this paper, we examine the Hyers–Ulam stability of two-dimensional convex mappings by using the sandwich theorem. Our next step involves the development of Hermite–Hadamard inequality, including its weighted and product forms, by using a novel type of fractional operator having non-singular kernels. Moreover, we develop several nontrivial examples and remarks to demonstrate the validity of our main results. Finally, we examine approximate convex mappings and have left an open problem regarding the best optimal constants for two-dimensional approximate convexity. Full article

This paper proposes a simple yet accurate finite element (FE) formulation for the thermomechanical analysis of laminated composites and sandwich plates. To this end, an enhanced first-order shear deformation theory including the transverse normal effect based on the mixed variational theorem (EFSDTM_TN) was employed in the FE implementation. The primary objective of the FE formulation was to systematically interconnect the displacement and transverse stress fields using the mixed variational theorem (MVT). In the MVT, the transverse stress field is derived from the efficient higher-order plate theory including the transverse normal effect (EHOPT_TN), to enhance the solution accuracy, whereas the displacement field is defined by the first-order shear deformation theory including the transverse normal effect (FSDT_TN), to amplify the numerical efficiency. Furthermore, the transverse displacement field is modified by incorporating the components of the external temperature loading, enabling the consideration of the transverse normal strain effect without introducing additional unknown variables. Based on the predefined relationships, the proposed FE formulation can extract the C0-based computational benefits of FSDT_TN, while improving the solution accuracy for thermomechanical analysis. The numerical performance of the proposed FE formulation was demonstrated by comparing the obtained solutions with those available in the literature, including 3-D exact solutions. Full article

The notions of strong differential subordination and its dual, strong differential superordination, have been introduced as extensions of the classical differential subordination and superordination concepts, respectively. The dual theories have developed nicely, and important results have been obtained involving different types of operators and certain hypergeometric functions. In this paper, quantum calculus and fractional calculus aspects are added to the study. The well-known q-hypergeometric function is given a form extended to fit the study concerning previously introduced classes of functions specific to strong differential subordination and superordination theories. Riemann–Liouville fractional integral of extended q-hypergeometric function is defined here, and it is involved in the investigation of strong differential subordinations and superordinations. The best dominants and the best subordinants are provided in the theorems that are proved for the strong differential subordinations and superordinations, respectively. For particular functions considered due to their remarkable geometric properties as best dominant or best subordinant, interesting corollaries are stated. The study is concluded by connecting the results obtained using the dual theories through sandwich-type theorems and corollaries. Full article

Due to the influence of mass law, traditional lightweight sandwich structures have struggled to surpass solid structures in sound insulation performance. To this end, we propose an acoustic metamaterial structure with a sandwich configuration based on the re-entrant negative Poisson’s ratio (NPR) structure and systematically investigate its sound transmission loss (STL) performance under incident plane wave conditions. We used the acoustic impedance tube method to experimentally study the sound insulation performance of the re-entrant NPR sandwich structure under free boundary conditions, and then established an acoustic analysis simulation model based on COMSOL Multiphysics software, which verified that the results obtained by the experiment and the numerical simulation were in good agreement. The results show that the sandwich structure exhibits excellent sound transmission loss performance in the studied frequency range (250–4000 Hz), and the overall sound insulation performance exceeds the curve of the mass theorem, basically achieving more than 20 dB when the sandwich thickness is 2 cm. Finally, we conduct parametric studies to establish a correlation between the geometric design of NPR sandwich structures and their sound transmission loss performance. The research shows that the changes of the length of the ribs, the distance from the ribs to the center of the unit, and the length of the upper wall and the lower wall have a significant impact on the sound insulation performance of the re-entrant NPR sandwich structure, while the change of the wall thickness basically will not affect the sound insulation performance of the sandwich structure. This research can provide practical ideas for the engineering application of noise suppression designs of lightweight structures. Full article

This article presents a new q-analog integral operator, which generalizes the q-Srivastava–Attiya operator. Using this q-analog operator, we define a family of analytic non-Bazilevič functions, denoted as ${\mathcal{T}}_{q,\tau +1,u}^{\mu }(\vartheta ,\lambda ,\mathcal{M},\mathcal{N})$. Furthermore, we investigate the differential subordination properties of univalent functions using q-calculus, which includes the best dominance, best subordination, and sandwich-type properties. Our results are proven using specialized techniques in differential subordination theory. Full article

Locally resonant phononic crystals are a kind of artificial periodic composite material/structure with an elastic wave band gap that show attractive application potential in low-frequency vibration control. For low-frequency vibration control problems of ship power systems, this paper proposes a phononic crystal board structure, and based on the Bloch theorem of periodic structure, it uses a finite element method to calculate the band structure and the displacement fields corresponding to the characteristic mode and vibration transmission curve of the corresponding finite periodic sandwich plate structure, and the band gap characteristics are studied. The mechanism of band gap formation is mainly attributed to the mode coupling of the phononic crystal plate structure. Numerical results show that the sandwich plate structure has a double periodicity, so it has a multi-stage elastic wave band gap, which can fully inhibit the transmission of flexural waves and isolate the low-frequency flexural vibration. The experimental measurements of flexural vibration transmission spectra were conducted to validate the accuracy and reliability of the numerical calculation method. On this basis, the potential application of the proposed vibration isolation method in a marine power system is discussed. A vibration isolation platform mounted on a steel plate is studied by numerical simulation, which can isolate low-frequency vibration to protect electronic equipment and precision instruments. Full article

In this paper, we discuss and introduce a new study using an integral operator $w_{k,\mu }^m$ in geometric function theory, especially sandwich theorems. We obtained some conclusions for differential subordination and superordination for a new formula generalized integral operator. In addition, certain sandwich theorems were found. The differential subordination theory’s features and outcomes are symmetric to those derived using the differential subordination theory. Full article