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Adequate mathematical description of magnetization curves is indispensable in engineering. The accuracy of the description has a significant impact on the design of electric machines and devices. The aim of this paper was to analyze the capability of Bézier curves systematically, to describe the nonlinear static magnetic properties of non-oriented electrical steels, and to compare this approach versus the established mathematical descriptions. First, analytic functions versus measurements were analyzed. The Bézier curves were then compared systematically with the most adequate analytic functions. Next, the most suitable orders of Bézier curves were determined for the approximation of nonlinear magnetic properties, where the influence of the range of the input measurement dataset on the approximation process was analyzed. Last, the extrapolation capabilities of the Bézier curves and analytic functions were evaluated. The general conclusion is that Bézier curves have adequate flexibility and significant potential for the approximation and extrapolation of nonlinear properties of non-oriented electrical steels. [ABSTRACT FROM AUTHOR]

In this paper, we consider the representation and extension of the analytic functions of three variables by special families of functions, namely branched continued fractions. In particular, we establish new symmetric domains of the analytical continuation of Lauricella–Saran's hypergeometric function  F K  with certain conditions on real and complex parameters using their branched continued fraction representations. We use a technique that extends the convergence, which is already known for a small domain, to a larger domain to obtain domains of convergence of branched continued fractions and the PC method to prove that they are also domains of analytical continuation. In addition, we discuss some applicable special cases and vital remarks. [ABSTRACT FROM AUTHOR]

In this study, we introduce a new class of normalized analytic and bi-univalent functions denoted by D Σ (δ , η , λ , t , r) . These functions are connected to the Bazilevič functions and the λ -pseudo-starlike functions. We employ Sakaguchi Type Functions and Horadam polynomials in our survey. We establish the Fekete-Szegö inequality for the functions in D Σ (δ , η , λ , t , r) and derive upper bounds for the initial Taylor–Maclaurin coefficients | a 2 | and | a 3 | . Additionally, we establish connections between our results and previous research papers on this topic. [ABSTRACT FROM AUTHOR]

In this paper, we consider a supersymmetric version of block-symmetric polynomials on a Banach space of two-sided absolutely summing series of vectors in C s for some positive integer s > 1. We describe some sequences of generators of the algebra of block-supersymmetric polynomials and algebraic relations between the generators for the finite-dimensional case and construct algebraic bases of block-supersymmetric polynomials in the infinite-dimensional case. Furthermore, we propose some consequences for algebras of block-supersymmetric analytic functions of bounded type and their spectra. Finally, we consider some special derivatives in algebras of block-symmetric and block-supersymmetric analytic functions and find related Appell-type sequences of polynomials. [ABSTRACT FROM AUTHOR]

In this paper, the structural properties of a function are characterized by moduli of continuity. The classical Hardy–Littlewood theorem describes a relation between the smoothness of the analytic function boundary values at the boundary of its analyticity and the growth rate of the modulus of its higher-order derivatives. An analogue of the Hardy–Littlewood theorem has been obtained for functions from the class Hp and higher-order moduli of continuity. [ABSTRACT FROM AUTHOR]

This paper aims to study the Geometric properties of analytic function in the open unit disk. In the present investigation, we obtain some geometric properties of Pascal distribution involving Kamali type related to leaf like domain. In this paper, we find coefficient inequality, Radii Properties, convolution product, partial sum of the class Σ (δ , Φ , β , s , t , m) . Furthermore, we examine the distortion bounds belonging to the same class. This paper aims to study the Geometric properties of analytic function in the open unit disk. In the present investigation, we obtain some geometric properties of Pascal distribution involving Kamali type related to leaf like domain. In this paper, we find coefficient inequality, Radii Properties, convolution product, partial sum of the class . Furthermore, we examine the distortion bounds belonging to the same class. [ABSTRACT FROM AUTHOR]

In this paper we consider a class of functions Mα (φ) defined by subordination, consisting of functions f G A satisfying the condition (1 - α) zf'(z)/f(z) + α (1 + zf"(z)/f'(z) ) < φ(z), z ∈ U. In the study of univalent functions, estimates on the Taylor coefficients are usually given. Another significant problem deals with the estimates of logarithmic coefficients. For the class S of univalent functions no sharp bounds for the modulus of the individual logarithmic coefficients are known if n ≥ 3. For different subclasses of S the results are not better and in most cases only the first three initial coefficients of log f(z)/z are considered. For the class Mα (φ) we obtain upper bounds for the logarithmic coefficients γn, n ∈ {1, 2, 3} and also for Γn, n ∈ {1, 2, 3}, the logarithmic coefficients of the inverse of Mα (φ). Connections with previous known results are pointed out. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions using the q-derivative operator D q 0 < q < 1 and the Gegenbauer polynomials in a symmetric domain, which is the open unit disc Λ = ℘ : ℘ ∈ C and ℘ < 1. For these subclasses of analytic and bi-univalent functions, the coefficient estimates and Fekete–Szegö inequalities are solved. Some special cases of the main results are also linked to those in several previous studies. The symmetric nature of quantum calculus itself motivates our investigation of the applications of such quantum (or q-) extensions in this paper. [ABSTRACT FROM AUTHOR]

In this paper we establish uncertainty inequality of Heisenberg type for Hardy space H, Dirichlet space D and Bergman space B, respectively. Next, we introduce a weighted Hardy space Hβ. This space which gives a generalization of some Hilbert spaces of analytic functions on the unit disk like, the Hardy space H, the Dirichlet space D and the Bergman space B, it plays a background to our contribution. Especially, we study the derivative operator D and its adjoint operator Lβ on Hβ, and we deduce a general uncertainty inequality of Heisenberg type for this space. [ABSTRACT FROM AUTHOR]

It is very well-known that the special functions and integral operators play a vital role in the research of applied and mathematical sciences. In this paper, our aim is to present sufficient conditions for the families of integral operators containing the normalized forms of the Miller–Ross functions such that they can be univalent in the open unit disk. Moreover, we find the convexity order of these operators. In proof of results, we use some differential inequalities related with Miller–Ross functions and well-known lemmas. The various results, which are established in this paper, are presumably new, and their importance is illustrated by several interesting consequences and examples. [ABSTRACT FROM AUTHOR]

In this paper we Ąnd bounds on the modulii of the second, third and fourth Taylor-Maclaurin's coefficients for functions in a subclass of bi-close-to-convex analytic functions, which includes the class studied by Srivastava et al. as particular case. Our estimates on the second and third coefficients improve upon earlier bounds. The result on the fourth coefficient is new. Our bounds are obtained by reĄning well known estimates for the initial coefficients of the Carthéodory functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new subclasses ... and of analytic functions in the open unit disk with negative coefficients defined by generalized Mittag-Leffler function. The object of the present paper is to determine coefficient inequalities, inclusion relations and neighborhoods properties for functions belonging to these subclasses. [ABSTRACT FROM AUTHOR]

The main target of this paper is to find out the estimates of the order and type of a bicomplex valued entire function. Also the famous Lucas's theorem on the zeros of a polynomial is deduced in the light of bicomplex analysis. A result is proved to show that the order and type remain invariant under differentiation of an entire function in C2. Also we prove some results related to Hadamard composition of two entire functions in C2. In fact, we find out here an estimate of the type of the Hadamard composition of two bicomplex valued entire functions. Also we show that the zeros of the derivative of a polynomial P(z) in C2 are contained within the convex hull of the zeros of P(z). Some examples are provided to justify the results obtained here. [ABSTRACT FROM AUTHOR]

According to Lidstone's interpolation theory, an entire function of a single variable of exponential type < π is determined by it derivatives of even order at 0 and 1. In a previous paper, we gave a survey of this classical univariate theory. Here, we generalize it to two variables. Multivariate Lidstone interpolation will be the topic of a forthcoming paper. [ABSTRACT FROM AUTHOR]

This article aims to provide a comprehensive analysis of the Taylor, Maclaurin, Lagrange, and other power series. A significant aspect is the exploration of Mansour's Expansion, a generalization of the work of Taylor, Maclaurin, and others in the realm of power series. This paper demonstrates how Taylor and Maclaurin's Expansion can be viewed as a special case of this new Expansion, which is an intriguing concept. Establishing this relationship provides a fresh perspective on these classical power series and their applications. In addition to exploring the relationships between classical power series, this article also highlights the practical applications of Mansour's Expansion. One key advantage of this new Expansion is its efficient algorithm, which quickly determines whether a polynomial is a composition. Furthermore, the algorithm can determine if a given polynomial g is a function in f. These capabilities carry significant implications for solving and simplifying polynomial functions into lower-degree functions. Mansour's Expansion provides a promising avenue for developing more efficient and effective methods for solving complex mathematical problems. It also provides a unique technique for solving an equation of the form f(x) = 0 not only by algebra, but also by iteration. It is an intriguing generalization of the work of Newton's Method. This makes it an important area of research for mathematicians and scientists alike. [ABSTRACT FROM AUTHOR]

Gegenbauer polynomials constitute a numerical tool that has attracted the interest of many function theorists in recent times mainly due to their real-life applications in many areas of the sciences and engineering. Their applications in geometric function theory (GFT) have also been considered by many researchers. In this paper, this powerful tool is associated with the prolific concepts of convolution and subordination. The main purpose of the research contained in this paper is to introduce and study a new subclass of analytic functions. This subclass is presented using an operator defined as the convolution of the generalized distribution and the error function and applying the principle of subordination. Investigations into this subclass are considered in connection to Carathéodory functions, the modified sigmoid function and Bell numbers to obtain coefficient estimates for the contained functions. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the sharp and accurate bounds for the logarithmic coefficients of some subclasses of analytic functions defined and studied in earlier works. Furthermore, we obtain the bounds of the second Hankel determinant of logarithmic coefficients for a class defined by subordination, such as the class of starlike functions  S * (φ) . Some applications of our results, which are extensions of those reported in earlier papers are given here as special cases. In addition, the results given can be used for other popular subclasses. [ABSTRACT FROM AUTHOR]

In the present paper, making use of the operator D p δ (λ , μ , l) , two new subclasses S λ , μ , l δ (A , B ; σ , p) and S T λ , μ , l δ (A , B ; σ , p) of p - valent functions are investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums and some applications of fractional calculus of functions belonging to each of these subclasses S λ , μ , l δ (A , B ; σ , p) and S T λ , μ , l δ (A , B ; σ , p) are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study certain geometric properties (like univalence, starlikeness, convexity, close-to-convexity) for the normalized Miller-Ross function. The various results, which we have established in the present investigation, are believed to be new, and their importance is illustrated by several interesting consequences and examples. Furthermore, some of the main results improve the corresponding results available in the literature [15]. [ABSTRACT FROM AUTHOR]

In this paper we prove some properties for functions that are multivalent in the unit disc |z| < 1 in the complex plane. As a corollary we obtain that if f(z) is p-valent, p ≥ 10, and |arg{f(p)(z)}|<π in |z| < 1, then f (z) is p-valent starlike. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, we study the inverse Sturm–Liouville problem with polynomials of the spectral parameter in the first boundary condition and with entire analytic functions in the second one. For the investigation of this new inverse problem, we develop an approach based on the construction of a special vector functional sequence in a suitable Hilbert space. The uniqueness of recovering the potential and the polynomials of the boundary condition from a part of the spectrum is proved. Furthermore, our main results are applied to the Hochstadt–Lieberman-type problems with polynomial dependence on the spectral parameter not only in the boundary conditions but also in discontinuity (transmission) conditions inside the interval. We prove novel uniqueness theorems, which generalize and improve the previous results in this direction. Note that all the spectral problems in this paper are investigated in the general non-self-adjoint form, and our method does not require the simplicity of the spectrum. Moreover, our method is constructive and can be developed in the future for numerical solution and for the study of solvability and stability of inverse spectral problems. [ABSTRACT FROM AUTHOR]

In this paper we show that each composition operator is isolated in comp(Lp) (1 ≤ p ≤ ∞) under the norm topology. We also prove that while each composition operator is non-isolated in comp(≤p) (1 ≤ p < ∞) under the strong operator topology, every composition operator is isolated in comp(L∞) under the strong operator topology. [ABSTRACT FROM AUTHOR]

Sanford S. Miller and Petru T. Mocanu's theory of second-order differential subordinations was extended for the case of third-order differential subordinations by José A. Antonino and Sanford S. Miller in 2011. In this paper, new results are proved regarding third-order differential subordinations that extend the ones involving the classical second-order differential subordination theory. A method for finding a dominant of a third-order differential subordination is provided when the behavior of the function is not known on the boundary of the unit disc. Additionally, a new method for obtaining the best dominant of a third-order differential subordination is presented. This newly proposed method essentially consists of finding the univalent solution for the differential equation that corresponds to the differential subordination considered in the investigation; previous results involving third-order differential subordinations have been obtained mainly by investigating specific classes of admissible functions. The fractional integral of the Gaussian hypergeometric function, previously associated with the theory of fuzzy differential subordination, is used in this paper to obtain an interesting third-order differential subordination by involving a specific convex function. The best dominant is also provided, and the example presented proves the importance of the theoretical results involving the fractional integral of the Gaussian hypergeometric function. [ABSTRACT FROM AUTHOR]

In recent years, with the continuous development and progress of wireless communication and sensors, people's production and life have also undergone tremendous changes. This article aims to apply wireless sensor networks to the construction of a supply–demand coordination innovation performance evaluation model, in order to improve its influence and application scope in real life. This paper deeply researches the architecture and node organization structure of wireless sensor network, and strengthens its theoretical foundation in the application of performance evaluation model. This paper designs performance evaluation indicators and compares performance evaluation methods at home and abroad based on the evaluation indicators, compares and analyzes the factor analysis method, fuzzy comprehensive evaluation method, comprehensive index evaluation method, etc., draws the advantages and disadvantages of each method, and uses them reasonably. The performance evaluation model constructed in this paper adopts the production function method and the analytic hierarchy process. According to the principles of scientificity, feasibility, and economy, the performance indicators for evaluating the balance of supply and demand are screened out, and score evaluation and comparison of each indicator are carried out. Finally, this paper analyzes the corporate performance evaluation index composition, model regression, sensor performance and performance evaluation scores, etc., and has a comprehensive application analysis of the model constructed in this paper. As can be seen from the overall score we selected five companies, enterprises composite score is 83.574, ranking first, followed by a score of 78.421. [ABSTRACT FROM AUTHOR]

In this paper, we employ a q -Noor integral operator to perform a q -analogue of certain fractional integral operator defined on an open unit disc. Then, we make use of the Hadamard convolution product to discuss several related results. Also, we derive a class of convex functions by utilizing the q -fractional integral operator and apply the inspired presented theory of the differential subordination, to geometrically explore the most popular differential subordination properties of the aforementioned operator. In addition, we discuss an exciting inclusion for the given convex class of functions. Over and above, we investigate the q -fractional integral operator and obtain some applications for the differential subordination. [ABSTRACT FROM AUTHOR]

Let A p n be the class of functions f z given by f z = z p + a p + n z p + n + a p + n + 1 z p + n + 1 + ⋯ which are analytic in the open unit disk U. For f z ∈ A p n , new integral operators O − j f z and O j f z j = 0 , 1 , 2 , ⋯. are considered. The operators O − j f z and O j f z satisfy O j O − j f z = O − j O j f z = f z and O − j ∗ O j f z = O j ∗ O − j f z = f ∗ f z for the convolution ∗ of O − j f z and O j f z. In the present paper, the dominants for both operators O − j f z and O j f z and subordinations for O − j f z and O j f z are discussed. Also, new subclass T p γ m , δ , ρ ; m , j concerning with m different boundary points is defined and discussed. Moreover, some interesting problems of T p γ m , δ , ρ ; m , j associated with O j f z are obtained. Furthermore, some interesting examples for our results are considered. [ABSTRACT FROM AUTHOR]

Recently, a number of researchers from different fields have taken a keen interest in the domain of fractional q-calculus on the basis of fractional integrals and derivative operators. This has been used in various scientific research and technology fields, including optics, mathematical biology, plasma physics, electromagnetic theory, and many more. This article explores some mathematical applications of the fractional q-differential and integral operator in the field of geometric function theory. By using the linear multiplier fractional q-differintegral operator D q , λ m ρ , σ and subordination, we define and develop a collection of q-starlike functions that are linked to the cardioid domain. This study also investigates sharp inequality problems like initial coefficient bounds, the Fekete–Szego problems, and the coefficient inequalities for a new class of q-starlike functions in the open unit disc U. Furthermore, we analyze novel findings with respect to the inverse function (μ − 1) within the class of q-starlike functions in U. The findings in this paper are easy to understand and show a connection between present and past studies. [ABSTRACT FROM AUTHOR]

In recent years, the problem of finding the sharp radii bounds for certain properties in geometric function theory has attracted several researchers. However, there are several instances where only lower bounds for the radius problems have been established. In this paper, we have worked in a similar direction to compute the upper bounds in these cases which coincides with the conjectured values. Moreover, explicit functions are provided which yield that these bounds are attainable. [ABSTRACT FROM AUTHOR]

In this paper, using a meromorphic univalent function of the form f(z) = 1 z−δ + ∞ k=j ak (z − δ)k, with missing coecients which has a simple pole at the point z = δ, 0 ≤ δ < 1, that is it is defined in U = U\ δ = z: z ∈ C and 0 < z − δ < 1, we note that for δ = 0 we obtain the class j of meromorphic functions. We define a new operator analogue of that of Aouf et al. [2] for univalent analytic functions defined in the open unit dick U and introduce new class of meromorphic univalent functions which for dierent values of its parameters many special new classes can be obtained from it. For this class of functions we obtained some of its properties such as coecient estimates, distortion theorem, the modified Hadamard product of two functions in it and also for function which its coecients are the sum of the squares of the coecients of two functions. Also we obtained analogue results of these results for each of the subclass obtained from this class. [ABSTRACT FROM AUTHOR]

In [6, 7], it was shown that mixed problems can be both ill-posed for Petrovsky well-conditioned equations and well-posed for ill-conditioned equations. In the present paper we study the existence and uniqueness of the solution of a mixed problem for a class of equations with complex-valued coefficients that behave as parabolic ones, despite the fact that they can change over "time" from parabolic type to Schrödinger type, or even to antiparabolic type. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce two new subclasses of the m-fold symmetric, analytic and bi-univalent function class Σm defined in the open unit disk D1:= {z: z ∈ C and |z| < 1}. These two subclasses are denoted by SΣm (α) and S*Σm (β). For the functions f belong to both of these subclasses, we obtain estimates on the first two Taylor-Maclaurin coefficients |am+1| and |a²m+1|. Also, we obtain estimate on the Fekete-Szegö functional |a2m+1 - ka 2 m+1 |, k ∈ R. It is interesting to see that the geometrical similarities in these two subclasses also reflects in their coefficient estimates. Further, we pointed out interconnection of these results with some of the earlier known results. [ABSTRACT FROM AUTHOR]

The concept of Lindelöf proximate order has been used extensively to study the functions of completely regular growth. The main drawback of this approach is that it completely ignores the value of lower order. To overcome this problem, Chyzykov et al. introduced the concept of generalized proximate order for irregular growth. In this paper we studied the existence of generalized proximate order for every functions analytic on the unit disc with some new results for functions having irregular growth. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to introduce a Wright distribution and obtain some sufficient conditions for analytic functions, whose coefficients are probabilities of the Wright distribution series, to belong to class of spiral-like univalent functions. Further, we discuss the geometric properties of an integral operator related to the Wright distribution series. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disc U = {z: z ∈ C and |z| < 1}. We find the bounds on the initial coefficients |c2| and |c3| and upper bounds for the Fekete-Szego functional for the functions in this class. [ABSTRACT FROM AUTHOR]

Let a normalized analytic function be given on the open unit disk. In this paper, we define and consider some familiar subsets of analytic functions associated with sine functions in the region of unit disk on the complex plane. For these classes, we aim to find the upper bounds of the modules of the Hankel determinants obtained from the coefficients of the functions belonging to some classes defined by subordination. [ABSTRACT FROM AUTHOR]

Appell's functions F1-F4 turned out to be particularly useful in solving a variety of problems in both pure and applied mathematics. In literature, there have been published a significant number of interesting and useful results on these functions. In this paper, we prove that the branched continued fraction, which is an expansion of ratio of hypergeometric functions F2converges uniformly to a holomorphic function of two variables on every compact subset of some domain of C²; and that this function is an analytic continuation of such ratio in this domain. As a special case of our main result, we give the representation of hypergeometric functions F2 by a branched continued fraction. To illustrate this, we have given some numerical experiments at the end. [ABSTRACT FROM AUTHOR]

In this paper, we determine the Hardy spaces of certain integral operators on normalised analytic functions defined in the open unit disk in the complex plane with the prior knowledge of the Hardy spaces of the functions or their derivatives in the integral. [ABSTRACT FROM AUTHOR]

The present paper defines a new subclass of analytic functions by means of the generalized polylogarithm equipped with subordination. The defined new class engages Poisson distribution series and generalized Pascal snail. The early first few coefficients are obtained and their relevance to classical inequality by Fekete-Szego are discussed. The consequences of our parametric equation are pointed out. [ABSTRACT FROM AUTHOR]

In this paper, the authors introduce and investigate a subclass of analytic functions Εm(β,λ,φ,γ ) (Ησ, α, δ, μ, l), satisfying certain subordinate condition associated with Gegenbauer polynomials. For the subclass introduced, we derive initial coefficients α2 and α3 and also obtain the classical Fekete-Szegë problem for functions in the subclass. Finally, our findings show relevant connections between our results and those in some earlier known investigations and obviously improve them. [ABSTRACT FROM AUTHOR]

In the present paper, we study the operator I (w, zw′; 2) = wγ {a+b/w+ cw + dzw/w′}; w ∈ D = C\{0}, z ∈ E, where E = {z; |z |<1} and a, b, c, d, β, γ be complex numbers such that d≠0, β≠ 0, to obtain superordination theorems which generalise and unify various well known results. In what follows, all the powers taken are the principle ones. [ABSTRACT FROM AUTHOR]

A bi-univalent function is a univalent function defined on the unit disc for which the inverse function has a univalent extension to the unit disc. In this paper, estimates for the initial as well as higher order coefficients |α4| and |α5| of bi-univalent functions belonging to certain class defined by subordination and of functions for which f and f −1 belong to different subclasses of univalent functions are derived. Generalization of existing known results were also pointed out. [ABSTRACT FROM AUTHOR]

In this paper, we present and investigate the notion of third-order strong differential subordinations, unveiling several intriguing properties within the context of specific classes of admissible functions. Furthermore, we extend certain definitions, presenting novel and fascinating results. We also derive several interesting properties of the results of third-order strong differential subordinations for analytic functions associated with the Srivastava–Attiya operator. [ABSTRACT FROM AUTHOR]

In this paper, we find sufficient conditions to be imposed on the parameters of a class of functions related to the Barnes–Mittag-Leffler function that allow us to conclude that it possesses certain geometric properties (such as starlikeness, uniformly starlike (convex), strongly starlike (convex), convexity, and close-to-convexity) in the unit disk. The key tools in some of our proofs are the monotonicity properties of a certain class of functions related to the gamma function. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new subclass of bi-univalent functions defined using Lucas-Balancing polynomials. For functions in each of these bi-univalent function subclasses, we derive estimates for the Taylor–Maclaurin coefficients a 2 and a 3 and address the Fekete–Szegö functional problems for functions belonging to this new subclass. We demonstrate that several new results can be derived by specializing the parameters in our main findings. The results obtained from this study will enrich the theoretical foundation of this field and open new avenues for mathematical inquiry and application. [ABSTRACT FROM AUTHOR]

In this paper we obtain coefficient characterization, extreme points and distortion bounds for the classes of p - valent harmonic functions defined by q - derivative operator. Some of our results improve and generalize previously known results. [ABSTRACT FROM AUTHOR]

This paper presents several properties and relations that satisfy the components of a bicomplex holomorphic function. It also exhibits several analogies and differences with the case of analytic functions. [ABSTRACT FROM AUTHOR]

In this paper, we studied some geometric properties of a class of analytic functions related to the generalized Mathieu type power series. Furthermore, we have identified interesting consequences and some examples accompanied by graphical representations to illustrate the results achieved. [ABSTRACT FROM AUTHOR]

In this paper, the harmonic function related to the q-Srivastava–Attiya operator is described to introduce a new class of complex harmonic functions that are orientation-preserving and univalent in the open-unit disk. We also cover some important aspects such as coefficient bounds, convolution conservation, and convexity constraints. Next, using sufficiency criteria, we calculate the sharp bounds of the real parts of the ratios of harmonic functions to their sequences of partial sums. In addition, for the first time some of the interesting implications of the q-Srivastava–Attiya operator in harmonic functions are also included. [ABSTRACT FROM AUTHOR]