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We define a new class of exponential starlike functions constructed by a linear operator involving normalized form of the generalized Struve function. Making use of a technique of differential subordination introduced by Miller and Mocanu, we investigate several new results related to the Briot–Bouquet differential subordinations for the linear operator involving the normalized form of the generalized Struve function. We also obtain univalent solutions to the Briot–Bouquet differential equations and observe that these solutions are the best dominant of the Briot–Bouquet differential subordinations for the exponential starlike function class. Moreover, we give an application of fractional integral operator for a complex-valued function associated with the generalized Struve function. The significance of this paper is due to the technique employed in proving the results and novelty of these results for the Struve functions. The approach used in this paper can lead to several new problems in geometric function theory associated with special functions. [ABSTRACT FROM AUTHOR]

In this paper, we discuss and introduce a new study on the connection between geometric function theory, especially sandwich theorems, and Viete's theorem in elementary algebra. We obtain some conclusions for differential subordination and superordination for a new formula of complete homogeneous symmetric functions class involving an ordered cyclic operator. In addition, certain sandwich theorems are found. [ABSTRACT FROM AUTHOR]

In the past few years, many scholars gave much attention to the use of q-calculus in geometric functions theory, and they defined new subclasses of analytic and harmonic functions. While using the symmetric q-calculus in geometric function theory, very little work has been published so far. In this research, with the help of fundamental concepts of symmetric q-calculus and the symmetric q-Salagean differential operator for harmonic functions, we define a new class of harmonic functions connected with Janowski functions S H 0 ˜ m , q , A , B . First, we illustrate the necessary and sufficient convolution condition for S H 0 ˜ m , q , A , B and then prove that this sufficient condition is a sense preserving and univalent, and it is necessary for its subclass TS H 0 ˜ m , q , A , B . Furthermore, by using this necessary and sufficient coefficient condition, we establish some novel results, particularly convexity, compactness, radii of q-starlike and q-convex functions of order α , and extreme points for this newly defined class of harmonic functions. Our results are the generalizations of some previous known results. [ABSTRACT FROM AUTHOR]

In geometric function theory, Lucas polynomials and other special polynomials have recently gained importance. In this study, we develop a new family of bi-univalent functions. Also we examined coefficient inequalities and Fekete-Szegö problem for this new family via these polynomials. [ABSTRACT FROM AUTHOR]

The geometric nonlinear response of spherical shells made of sandwich functionally graded material (SFGM) under uniform external pressure incorporating the effects of transverse shear deformations is considered. The equilibrium and compatibility nonlinear differential equations can be solved by using the modified interaction method. All of the equations are developed based on the first-order shear deformation theory (FSDT). In the present study, the geometric nonlinear problem has been solved for special boundary conditions including movable and fixed clamped supports in the meridional direction. A closed-form nonlinear load-deflection relationship is developed for SFGM shell which expresses the equilibrium path of the shell. [ABSTRACT FROM AUTHOR]

The word "symmetry" is a Greek word that originated from "symmetria". It means an agreement in dimensions, due proportion, and arrangement; however, in complex analysis, it means objects remaining invariant under some transformation. This idea has now been recently used in geometric function theory to modify the earlier classical q-derivative introduced by Ismail et al. due to its better convergence properties. Consequently, we introduce a new class of analytic functions by using the notion of q-symmetric derivative. The investigation in this paper obtains a number of the latest important results in q-theory, including coefficient inequalities and convolution characterization of q-symmetric starlike functions related to Janowski mappings. [ABSTRACT FROM AUTHOR]

Aspects related to applications in the geometric function theory of q-calculus are presented in this paper. The study concerns the investigation of certain q-analogue differential operators in order to obtain their geometrical properties, which could be further developed in studies. Several interesting properties of the q-analogue of the Sălăgean differential operator are obtained here by using the differential subordination method. [ABSTRACT FROM AUTHOR]

The topics studied in the geometric function theory of one variable functions are connected with the concept of Symmetry because for some special cases the analytic functions map the open unit disk onto a symmetric domain. Thus, if all the coefficients of the Taylor expansion at the origin are real numbers, then the image of the open unit disk is a symmetric domain with respect to the real axis. In this paper, we formulate the q-differential operator associated with the q-Raina function using quantum calculus, that is the so-called Jacksons' calculus. We establish a new subclass of analytic functions in the unit disk by using this newly developed operator. The theory of differential subordination inspired our approach; therefore, we geometrically explore the most popular properties of this new operator: subordination properties, coefficient bounds, and the Fekete-Szegő problem. As special cases, we highlight certain well-known corollaries of our primary findings. [ABSTRACT FROM AUTHOR]

Abstract. In Geometric Function Theory of Complex Analysis, there have been many interesting and fruitful usages of a wide variety of differential subordinations for holomorphic functions in the unit disk ...: ... Here, in this article, we derive some properties of the first-order differential subordinations for holomorphic functions which are defined in the unit ball ℝ: ... by using a certain class of admissible functions. We also make use of the theory of biholomorphic functions in our investigation here. [ABSTRACT FROM AUTHOR]

Ever since Lotfi A. Zadeh published the paper "Fuzzy Sets" in 1965 setting the basis of a new theory named fuzzy sets theory, many scientists have developed this theory and its applications. Mathematicians were especially interested in extending classical mathematical results in the fuzzy context. Such an extension was also done relating fuzzy sets theory and geometric theory of analytic functions. The study begun in 2011 has many interesting published outcomes and the present paper follows the line of the previous research in the field. The aim of the paper is to give some references related to the connections already made between fuzzy sets theory and geometric theory of analytic functions and to present some new results that might prove interesting for mathematicians willing to enlarge their views on certain aspects of the merge between the two theories. Using the notions of fuzzy differential subordination and the classical notion of differential subordination for analytic functions, two criteria for the univalence of the analytic functions are stated in this work. [ABSTRACT FROM AUTHOR]

Fractional differential operators are mostly investigated for functions of real variables. In this paper, we present two fractional differential operators for a class of normalized analytic functions in the open unit disk. The suggested operators are investigated according to concepts in geometric function theory, using the concepts of convexity and starlikeness. Therefore, we reformulate the new operators in the Ma-Minda class of analytic functions, in order to act on normalized analytic functions. Our method is based on subordination, superordination, and majorization theory. As an application, we employ these operators to generalize Bernoulli’s equation and a special class of Briot-Bouquet equations. The solution of the generalized equation is formulated by a hypergeometric function. [ABSTRACT FROM AUTHOR]

The Gould–Hopper–Laguerre–Sheffer matrix polynomials were initially studied using operational methods, but in this paper, we investigate them using matrix techniques. By leveraging properties of Pascal functionals and Wronskian matrices, we derive several identities for these polynomials, including recurrence relations. It is highlighted that these identities, acquired via matrix techniques, are distinct from the ones obtained when using operational methods.

The Neumann–Poincaré (NP) operator, a singular integral operator on the boundary of a domain, naturally appears when one solves a conductivity transmission problem via the boundary integral formulation. Recently, a series expression of the NP operator was developed in two dimensions based on geometric function theory [34]. In this paper, we investigate geometric properties of composite materials using this series expansion. In particular, we obtain explicit formulas for the polarisation tensor and the effective conductivity for an inclusion or a periodic array of inclusions of arbitrary shape with extremal conductivity, in terms of the associated exterior conformal mapping. Also, we observe by numerical computations that the spectrum of the NP operator has a monotonic behaviour with respect to the shape deformation of the inclusion. Additionally, we derive inequality relations of the coefficients of the Riemann mapping of an arbitrary Lipschitz domain using the properties of the polarisation tensor corresponding to the domain. [ABSTRACT FROM AUTHOR]

This short opus is dedicated to the bright memory of the distinguished mathematician Gabriela Kohr and her mathematical heritage. Gabriela KohPs contribution to analysis of one and several complex variables brought new knowledge into the modern theory as well as new colors to the subject. During our meetings with Gabriela at various conferences she always proposed some interesting and often nonstandard questions related to classical issues as well as new directions. It is worth to be mentioned her excellent book [50] together with Ian Graham on classical and modern problems in Geometric Function Theory in complex spaces (see also, [46], [56], [27], [22], [24], [49] and [48]). [ABSTRACT FROM AUTHOR]

In this paper we study the class of "shearing" holomorphic maps of the unit ball of the form (z,w)→ (z + g(w),w). Besides general properties, we use such maps to construct an example of a normalized univalent map of the ball onto a Runge domain in Cn which however cannot be embedded into a Loewner chain whose range is Cn. [ABSTRACT FROM AUTHOR]

We review the main contributions of Professor Gabriela Kohr in her studies in the Geometric function theory in several complex variables and complex Banach spaces with special emphasis on the theory of Loewner chains and the Loewner differential equation. [ABSTRACT FROM AUTHOR]

Fuzzy differential subordination theory represents a generalization of the classical concept of differential subordination which emerged in the recent years as a result of embedding the concept of fuzzy set into geometric function theory. The fractional integral of Gaussian hypergeometric function is defined in this paper and using properties of the subordination chains, new fuzzy differential subordinations are obtained. Dominants of the fuzzy differential subordinations are given and using particular functions as such dominants, interesting geometric properties interpreted as inclusion relations of certain subsets of the complex plane are presented in the corollaries of the original theorems stated. An example is constructed as an application of the newly proved results. [ABSTRACT FROM AUTHOR]

The Atangana–Baleanu fractional integral and multiplier transformations are two functions successfully used separately in many recently published studies. They were previously combined and the resulting function was applied for obtaining interesting new results concerning the theories of differential subordination and fuzzy differential subordination. In the present investigation, a new approach is taken by using the operator previously introduced by applying the Atangana–Baleanu fractional integral to a multiplier transformation for introducing a new subclass of analytic functions. Using the methods familiar to geometric function theory, certain geometrical properties of the newly introduced class are obtained such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity, and close-to-convexity of functions belonging to the class. This class may have symmetric or assymetric properties. The results could prove interesting for future studies due to the new applications of the operator and because the univalence properties of the new subclass of functions could inspire further investigations having it as the main focus. [ABSTRACT FROM AUTHOR]

In this article we obtain a factorization theorem for the functions in Paatero's V(k) space. We bring attention to a significant result of Pinchuk which unfortunately is false. This result relates measures associated to functions in V(k) and an integral representation theorem for such functions. We prove necessary and sufficient conditions for a wide class of functions (in particular, the polynomials) to belong to the Paatero class based on the geometry of their critical points, and obtain explicit representation of the measures associated to a wide class of such polynomials that includes the Suffridge polynomials. [ABSTRACT FROM AUTHOR]

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There are many classical results, related to the Denjoy–Wolff theorem, concerning the relationship between orbits of interior points and orbits of boundary points under iterates of holomorphic self-maps of the unit disc. Here, we address such questions in the very general setting of sequences (F n) of holomorphic maps between simply connected domains. We show that, while some classical results can be generalised, with an interesting dependence on the geometry of the domains, a much richer variety of behaviours is possible. One of our main results is new even in the classical setting. Our methods apply in particular to non-autonomous dynamical systems, when (F n) are forward compositions of holomorphic maps, and to the study of wandering domains in holomorphic dynamics. The proofs use techniques from geometric function theory, measure theory and ergodic theory, and the construction of examples involves a 'weak independence' version of the second Borel–Cantelli lemma and the concept from ergodic theory of 'shrinking targets'. [ABSTRACT FROM AUTHOR]

Various operators of fractional calculus, as well as their quantum (or q -) extensions have been used widely and successfully in the study of the Taylor-Maclaurin coefficient estimation problems for many different families of normalized analytic, univalent and bi-univalent functions in Geometric Function Theory of Complex Analysis. On the other hand, Numerous writers have extensively employed orthogonal polynomials in the framework of Geometric Function Theory in Complex analysis. The recent and ongoing studies on this topic is primarily what drives us. In this paper, we solve the Fekete-Szegö problem for the symmetric function classes of analytical and bi-univalent functions involving the Euler polynomials. We also give estimates for the coefficients and an upper bound for the second Hankel determinant. [ABSTRACT FROM AUTHOR]

Applications of the Atangana–Baleanu fractional integral were considered in recent studies related to geometric function theory to obtain interesting differential subordinations. Additionally, the multiplier transformation was used in many studies, providing elegant results. In this paper, a new operator is defined by combining those two prolific functions. The newly defined operator is applied for introducing a new subclass of analytic functions, which is investigated concerning certain properties, such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and radii of starlikeness, convexity and close-to-convexity. This class may have symmetric or asymmetric properties. The results could prove interesting due to the new applications of the Atangana–Baleanu fractional integral and of the multiplier transformation. Additionally, the univalence properties of the new subclass of functions could inspire researchers to conduct further investigations related to this newly defined class. [ABSTRACT FROM AUTHOR]

Recently, q-analogue of Noor integral operator and other special operators became importance in the field of Geometric Function Theory. In this study, by connecting this operators we introduced an interesting class of bi-univalent functions and obtained coefficient estimates for this new class. Also we present some relevant corollaries. [ABSTRACT FROM AUTHOR]

According to the theory of regular geometric functions, the relevance of geometry to analysis is a critical feature. One of the significant tools to study operators is to utilize the convolution product. The dynamic techniques of convolution have attracted numerous complex analyses in current research. In this effort, an attempt is made by utilizing the said techniques to study a new linear complex operator connecting an incomplete beta function and a Hurwitz–Lerch zeta function of certain meromorphic functions. Furthermore, we employ a method based on the first-order differential subordination to derive new and better differential complex inequalities, namely differential subordinations. [ABSTRACT FROM AUTHOR]

We consider the problem of extreme partition of the complex plane well known in the geometric theory of functions. We obtain estimates for the maximum value of the product of some powers of inner radii of n disjoint domains in the complex plane with respect to n arbitrary points of the plane one of which can be located at infinity. The estimates established in the paper can be applied to various problems of the geometric theory of functions. [ABSTRACT FROM AUTHOR]

An increasing homeomorphism h on the real line R is said to be strongly symmetric if it can be extended to a Quasiconformal homeomorphism of the upper half plane U onto itself whose Bcltrami coefficient µ induces a vanishing Carlcson measure\µ.(z')\2/y dxd.y on U. Wc will deal with the class of strongly symmetric homeomorphisms on the real line and its TcichmuJlcr space, which we call the VMO-Tcichmuller space. In particular, we will show that if h is strongly symmetric on the real line, then it is strongly quasisymmctric such that log h, is a VMO function. This improves some classical results of Carleson (1967) and Anderson-Bcckcr-Lesley (1988) on the problem about the local absolute continuity of a quasisymmetric homeomorphism in terms of the Bcltrami coefficient of a quasiconformal extension. Wc will also discuss various models of the VMO-Teichmiiller space and endow it with a complex Banach manifold structure via the standard Bers embedding. [ABSTRACT FROM AUTHOR]

This paper considers solving more than one combinatorial problem considered some of the most difficult to solve in the combinatorial optimization field, such as the job shop scheduling problem (JSSP), the vehicle routing problem with time windows (VRPTW), and the quay crane scheduling problem (QCSP). A hybrid metaheuristic algorithm that integrates the Mallows model and the Moth-flame algorithm solves these problems. Through an exponential function, the Mallows model emulates the solution space distribution for the problems; meanwhile, the Moth-flame algorithm is in charge of determining how to produce the offspring by a geometric function that helps identify the new solutions. The proposed metaheuristic, called HEDAMMF (Hybrid Estimation of Distribution Algorithm with Mallows model and Moth-Flame algorithm), improves the performance of recent algorithms. Although knowing the algebra of permutations is required to understand the proposed metaheuristic, utilizing the HEDAMMF is justified because certain problems are fixed differently under different circumstances. These problems do not share the same objective function (fitness) and/or the same constraints. Therefore, it is not possible to use a single model problem. The aforementioned approach is able to outperform recent algorithms under different metrics for these three combinatorial problems. Finally, it is possible to conclude that the hybrid metaheuristics have a better performance, or equal in effectiveness than recent algorithms. [ABSTRACT FROM AUTHOR]

We give an exposition of results from a crossroad between geometric function theory, harmonic analysis, boundary value problems, and approximation theory, which characterize quasicircles. We will specifically expose the interplay between the jump decomposition, singular integral operators, approximation by Faber series, and the Grunsky inequalities. Our unified point of view is made possible by the concept of transmission. [ABSTRACT FROM AUTHOR]

In quantum geometric Langlands, the Satake equivalence plays a less prominent role than in the classical theory. Gaitsgory and Lurie proposed a conjectural substitute, later termed the fundamental local equivalence. With a few exceptions, we prove this conjecture and its extension to the affine flag variety by using what amount to Soergel module techniques. [ABSTRACT FROM AUTHOR]

We explore the correspondence between geometric function theory (GFT) and quantum field theory (QFT). The crossing symmetric dispersion relation provides the necessary tool to examine the connection between GFT, QFT, and effective field theories (EFTs), enabling us to connect with the crossing-symmetric EFT-hedron. Several existing mathematical bounds on the Taylor coefficients of Typically Real functions are summarized and shown to be of enormous use in bounding Wilson coefficients in the context of 2-2 scattering. We prove that two-sided bounds on Wilson coefficients are guaranteed to exist quite generally for the fully crossing symmetric situation. Numerical implementation of the GFT constraints (Bieberbach-Rogosinski inequalities) is straightforward and allows a systematic exploration. A comparison of our findings obtained using GFT techniques and other results in the literature is made. We study both the three-channel as well as the two-channel crossing-symmetric cases, the latter having some crucial differences. We also consider bound state poles as well as massless poles in EFTs. Finally, we consider nonlinear constraints arising from the positivity of certain Toeplitz determinants, which occur in the trigonometric moment problem. [ABSTRACT FROM AUTHOR]

In this article, a new class ( ) of analytic functions which is defined by terms of a quasi-subordination is introduced. The coefficient estimates, including the classical - ̈ inequality of functions belonging to this class, are then derived. Also, several special improving results for the associated classes involving the subordination are presented. [ABSTRACT FROM AUTHOR]

This paper aims at introducing a new generalized differential operator and new subclass of analytic functions to obtain some interesting properties like coefficient estimates and fractional derivatives. [ABSTRACT FROM AUTHOR]

In the paper, the author presents bounds for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function. This result partially confirms one in a series of conjectures on completely monotonic degrees of remainders of asymptotic expansions for the logarithm of the gamma function and for polygamma functions. [ABSTRACT FROM AUTHOR]

The study of the Dirichlet problem with arbitrary measurable data for harmonic functions in the unit disk 𝔻 is due to the dissertation of Luzin. Later on, the known monograph of Vekua was devoted to boundary-value problems only with Hölder continuous data for generalized analytic functions, i.e., continuous complex-valued functions f(z) of the complex variable z = x + iy with generalized first partial derivatives by Sobolev satisfying equations of the form ∂ z ¯ f + af + b f ¯ = c , where the complexvalued functions a; b, and c are assumed to belong to the class Lp with some p > 2 in smooth enough domains D in ℂ. Our last paper [12] contained theorems on the existence of nonclassical solutions of the Hilbert boundaryvalue problem with arbitrary measurable data (with respect to logarithmic capacity) for generalized analytic functions f : D → ℂ such that ∂ z ¯ f = g with the real-valued sources. On this basis, the corresponding existence theorems were established for the Poincaré problem on directional derivatives and, in particular, for the Neumann problem to the Poisson equations △U = G ∈ Lp; p > 2, with arbitrary measurable boundary data over logarithmic capacity. The present paper is a natural continuation of the article [12] and includes, in particular, theorems on the existence of solutions for the Hilbert boundary-value problem with arbitrary measurable data for the corresponding nonlinear equations of the Vekua type ∂ z ¯ f z = h z q f z . On this basis, existence theorems were also established for the Poincar´e boundary-value problem and, in particular, for the Neumann problem for the nonlinear Poisson equations of the form △U(z) = H(z)Q(U(z)) with arbitrary measurable boundary data over logarithmic capacity. The Dirichlet problem was investigated by us for the given equations, too. Our approach is based on the interpretation of boundary values in the sense of angular (along nontangential paths) limits that are a conventional tool of the geometric function theory. As consequences, we give applications to some concrete semi-linear equations of mathematical physics arising from modelling various physical processes. Those results can also be applied to semi-linear equations of mathematical physics in anisotropic and inhomogeneous media. [ABSTRACT FROM AUTHOR]

There is a rich literature on estimation of second and third Hankel determinants for normalised analytic functions in geometric function theory. It is also, therefore, natural to explore the concept of the Hermitian–Toeplitz determinants for such functions. In this paper, the sharp lower and upper estimations for third-order Hermitian-Toeplitz determinant for functions with bounded turning of order α, are obtained. [ABSTRACT FROM AUTHOR]

The central purpose of this effort is to investigate analytic and geometric properties of a class of normalized analytic functions in the open unit disk involving Bernoulli's formula. As a consequence, some solutions are indicated by the well-known hypergeometric function. The class of starlike functions is investigated containing the suggested class. [ABSTRACT FROM AUTHOR]

Recently the author has presented a new approach to solving the coefficient problems for holomorphic functions based on the deep features of Teichmüller spaces. It involves the Bers isomorphism theorem for Teichmüller spaces of punctured Riemann surfaces. The aim of the present paper is to provide new applications of this approach and extend the indicated results to more general classes of functions [ABSTRACT FROM AUTHOR]

The motivation of the present paper is to define q-analogue of Wanas operator in geometric function theory. We also introduce certain families T; m (t; n; fi; q;) and T; m (t; n; fi; q;) of holormorphic and m-fold symmetric bi-univalent functions associated with q-analogue of Wanas operator. The upper bounds for the second and third Taylor-Maclaurin coefficients for functions in each of these subfamilies are obtained. Furthermore, Several consequences of our results are pointed out based on the various special choices of the involved parameters. [ABSTRACT FROM AUTHOR]

Recently considerable effort has been devoted to the study of fractional calculus in many branches of mathematics and physics. The main object of the present investigation is to provide a brief survey concerning fractional integral and derivative operators in Geometric Function Theory. The generalizations of these operators are also concerned along with numerous properties of these generalized operators. We also list some samples which reflect our recent investigations in the Geometric Function Theory. [ABSTRACT FROM AUTHOR]

In this note, we formulate a new linear operator given by Airy functions of the first type in a complex domain. We aim to study the operator in view of geometric function theory based on the subordination and superordination concepts. The new operator is suggested to define a class of normalized functions (the class of univalent functions) calling the Airy difference formula. As a result, the suggested difference formula joining the linear operator is modified to different classes of analytic functions in the open unit disk. [ABSTRACT FROM AUTHOR]

Recently, there have been many new results on Schur convexity of integral means. In this paper we investigate the necessary and sufficient conditions for the existence of Schur-geometric and Schur-harmonic properties in weighted integral means, weighted midpoint and weighted trapezoid quadrature formulas. [ABSTRACT FROM AUTHOR]

Given a nonempty compact set in a proper subdomain of the complex plane, we denote the diameter of and the distance from to the boundary of by and , respectively. The quantity is invariant under similarities and plays an important role in geometric function theory. In case has the hyperbolic distance , we consider the infimum of the quantity over compact subsets of with at least two points, where stands for the hyperbolic diameter of . Let the upper half-plane be . We show that is positive if and only if the boundary of is uniformly perfect and for all , with equality holding precisely when is convex. [ABSTRACT FROM AUTHOR]

Recently, q-analogue of Noor integral operator and other special operators became importance in the field of Geometric Function Theory. In this study, by connecting this operators and the principle of subordination we introduced an interesting class of bi-univalent functions and obtained coefficient estimates for this new class. [ABSTRACT FROM AUTHOR]

In this present paper, we obtain some differential subordination and superordination results, by using generalized operators for certain subclass of analytic functions in the open unit disk. Also, we derive some sandwich results. [ABSTRACT FROM AUTHOR]

Recently, there has been a vivid interest on special functions from the point of view of geometric function theory. Geometric properties of special functions like univalency, starlikeness and convexity appear in works of many mathematicians. In this paper, firstly, we obtain a new family of integral operators involving normalized Mittag-Leffler functions. Then, we give various sufficient conditions for convexity of this integral operator in the open unit disk. Several consequences of the main results are also shown. [ABSTRACT FROM AUTHOR]

We consider a well-known problem of the geometric theory of functions on the extreme partition of the complex plane. For this problem, we establish estimates for the maximum value of the product of inner radii of n nonoverlapping domains with respect to n arbitrary points in the complex plane one of which may be infinitely remote. At present, the exact solutions of this problem are known only for n = 2, 3, 4. We establish estimates that can be used in various extreme problems of the geometric theory of functions. [ABSTRACT FROM AUTHOR]