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The key purpose of this paper is to investigate the Bohr radius for several subclasses of analytic functions with negative coefficients. Our investigation with the Bohr radius correlates with the classes of generalized Janowski type functions. Under this novel strategy, we develop Bohr's phenomenon for a generalized class associated with q-functions having q 2 (0; 1). In the applications viewpoint, our consequences have shown the applicability in the class inaugurated by Bessel functions. [ABSTRACT FROM AUTHOR]

We consider a quite general problem from the geometric theory of functions, namely, the problem of finding the maximal value of the product of inner radii of n nonoverlapping domains that contain points of the unit circle and are symmetric with respect to this circle and the γ power of the inner radius of a domain containing the origin. The posed problem is solved for n ≥ 20 and 1 < γ ≤ n 2 3 − q n . [ABSTRACT FROM AUTHOR]

In this work, we introduce and investigate an interesting operator Q based on fractional derivative which is introduced by Owa and Srivastava in [10]. We consider a new technique to prove our results and then, we introduce two subclasses of analytic functions in the open unit disk U concerning with this operator. Some results such as inclusion relations, subordination properties, integral preserving properties and argument estimate are investigated. [ABSTRACT FROM AUTHOR]

In the present paper, I have introduced the concept of fuzzy anti n-inner product function on a linear space and discussed its properties. Fuzzy anti n-inner product has been defined relative to fuzzy anti n-norm. Lastly Parallelogram law and polarization identity has been proved. [ABSTRACT FROM AUTHOR]

The effect of suspended particles, couple stress and permeability of the medium on the thermal instability of a couple stress Rivlin-Ericksen ferromagnetic fluid with varying gravity fields through a porous medium are investigated. The dispersion relation has been developed and solved analytically using the normal mode approach and linear stability theory. For stationary conventions, it is found that suspended particles always have a destabilizing effect if λ > 0 and a stabilizing effect if λ < 0. Couple stress has a stabilizing effect if λ > 0 and a destabilizing effect if λ < 0. Permeability has a stabilizing effect if λ < 0 and a destabilizing effect if λ > 0. Magnetization always has a stabilizing effect either λ > 0 or λ < 0. Oscillatory modes are not allowed and the principle of exchange of stability is satisfied. [ABSTRACT FROM AUTHOR]

We provide an analytical solution for the elastic fields in a two-dimensional unbounded isotropic body with a rigid inclusion. Our analysis is based on the boundary integral formulation of the elastostatic problem and geometric function theory. Specifically, we use the coordinate system provided by the exterior conformal mapping of the inclusion to define a density basis functions on the boundary of the inclusion, and we use the Faber polynomials associated with the inclusion for a basis inside the inclusion. The latter, which constitutes the main novelty of our approach, allows us to obtain an explicit series solution for the plane elastostatic problem for an inclusion of arbitrary shape in terms of the given arbitrary far-field loading. [ABSTRACT FROM AUTHOR]

Bieberbach's conjecture was very important in the development of geometric function theory, not only because of the result itself, but also due to the large amount of methods that have been developed in search of its proof. It is in this context that the integral transformations of the type f α (z) = ∫ 0 z (f (ζ) / ζ) α d ζ or F α (z) = ∫ 0 z (f ′ (ζ)) α d ζ appear. In this note we extend the classical problem of finding the values of α ∈ C for which either f α or F α are univalent, whenever f belongs to some subclasses of univalent mappings in D , to the case of logharmonic mappings by considering the extension of the shear construction introduced by Clunie and Sheil-Small in (Clunie and Sheil-Small in Ann. Acad. Sci. Fenn., Ser. A I 9:3–25, 1984) to this new scenario. [ABSTRACT FROM AUTHOR]

Abstract. We consider the conductivity transmission problem in two dimensions with a simply connected inclusion of arbitrary shape. It is well known that the solvability of the transmission prob- lem can be established via the boundary integral formulation in which the Neumann-Poincar\e (NP) operator is involved. In this paper, we derive series expansions of the layer potential operators based on geometric function theory and exhibit a novel approach to the transmission problem. We frst construct a collection of harmonic basis functions by using the Faber polynomials associated with the simply connected inclusion. We then derive explicit series expansions of the layer potential operators with respect to the constructed basis functions. In particular, the NP operator becomes a doubly infnite, self-adjoint matrix operator, whose entry is explicitly given by the Grunsky coefcients cor- responding to the inclusion. By applying the fnite section method to this matrix formulation, we obtain an approximation scheme for the spectrum of the NP operator and the solution to the trans- mission problem. This scheme allows us to numerically compute, in a simple way, the spectrum of the NP operator for a smooth domain when the exterior conformal mapping is known. We additionally derive an explicit integral expression for the coefcients of the exterior conformal mapping so that for an inclusion of arbitrary shape, one can numerically compute the exterior conformal mapping by solving only one boundary integral equation and apply the proposed approach. We provide numerical examples to demonstrate the efectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A typical quandary in geometric functions theory is to study a functional composed of amalgamations of the coefficients of the pristine function. Conventionally, there is a parameter over which the extremal value of the functional is needed. The present paper deals with consequential functional of this type. By making use of Hohlov operator, a new subclass ℛ a , b c of analytic functions defined ins the open unit disk is introduced. For both real and complex parameter, the sharp bounds for the Fekete–Szegö problems are found. An attempt has also been taken to found the sharp upper bound to the second and third Hankel determinant for functions belonging to this class. All the extremal functions are express in term of Gauss hypergeometric function and convolution. Finally, the sufficient condition for functions to be in ℛ a , b c is derived. Relevant connections of the new results with well-known ones are pointed out. [ABSTRACT FROM AUTHOR]

In the geometric theory of functions of a complex variable, the well-known direction is related to the estimates of the products of the inner radii of pairwise nonoverlapping domains. This direction is called extreme problems in classes of pairwise nonoverlapping domains. One of the problems of this type is considered in the present work. [ABSTRACT FROM AUTHOR]

In this paper, we describe the inhomogeneous Hilbert boundary-value problem of the theory of analytic functions with an infinite index and a boundary condition for a half-plane. The coefficients of the boundary condition are Hölder-continuous everywhere except for a finite number of singular points at which the argument of the coefficient function has second-type discontinuities (of a power order with exponent <1). We obtain formulas for the general solution of the inhomogeneous problem and discuss the existence and uniqueness of the solution. The study is based on the theory of entire functions and the geometric theory of functions of a complex variable. [ABSTRACT FROM AUTHOR]

The objective of this paper is to obtain an upper bound to the third Hankel determinant for certain subclass of p-valent functions, using Toeplitz determinants. [ABSTRACT FROM AUTHOR]

The paper is devoted to an extremal problem of geometric function theory of complex variable related with estimate of functional defined on system of mutually non-overlapping domains. An improved method is proposed for solving problems on extremal decomposition of the complex plane. The main results of the paper generalize and strengthening all known results in this problem for n-radial systems of points. In particular, the problem on extremal decomposition of the complex plane is solved for two free poles. [ABSTRACT FROM AUTHOR]

In this work, bi-univalent functions, which are one of the most important research areas of Geometric Function Theory and which are still very popular in recent years, have been investigated. For the studies of functions, it is customary to determine the bound. In this direction, firstly, we introduce a new subclass of bi-univalent functions in the open unit disk D = {z ∈ C: /z/ < 1}. For this purpose, the Komatu integral operator developed for complex functions and subordination princible are used. Afterwards, the relation between the Fibonacci number sequence and the functions with the positive real part is given. This relation is a fundamental role for Results section. The upper bounds of the first two Taylor-Maclaurin coefficients are investigated. Finally, we derive Fekete-Szegö inequalities for functions belonging to this newly-defined class. The obtained results are compared with studies in the literature. [ABSTRACT FROM AUTHOR]

In this particular work, we define a modified q-sigmoid function and use the mean function to study the convex and concave properties. We further apply the modified q-sigmoid function to geometric function theory defined in a complex plane with examples. [ABSTRACT FROM AUTHOR]

Non extreme points of compact, convex integral families of analytic functions are investigated. Knowledge about extreme points provides a valuable tool in the optimization of linear extremal problems. The functions studied are determined by a 2-parameter collection of kernel functions integrated against measures on the torus. Families from classical geometric function theory such as the closed convex hull of the derivatives of normalized close-to-convex functions, the ratio of starlike functions of different orders, as well as many others are included. However for these families of analytic functions, identifying "all" the extreme points remains a difficult challenge except in some special cases. Aharonov and Friedland [1] identified a band of points on the unit circle which corresponds to the set of extreme points for these 2-parameter collections of kernel functions. Later this band of extreme points was further extended by introducing a new technique by Dow and Wilken [3]. On the other hand, a technique to identify a non extreme point was not investigated much in the past probably because identifying non extreme points does not directly help solving the optimization of linear extremal problems. So far only one point on the unit circle has been identified which corresponds to a non extreme point for a 2-parameter collections of kernel functions. This leaves a big gap between the band of extreme points and one non extreme point. The author believes it is worth developing some techniques, and identifying non extreme points will shed a new light in the exact determination of the extreme points. The ultimate goal is to identify the point on the unit circle that separates the band of extreme points from non extreme points. The main result introduces a new class of non extreme points. [ABSTRACT FROM AUTHOR]

Analytic functions are characterized by the geometry of their image domains. That's why, geometry of image domain is of substantial importance to have a comprehensive study of analytic functions. To introduce and study new geometrical structures as image domain and to define their subsequent analytic functions is an ongoing part of research in geometric function theory. We introduced a new domain named as cardioid domain and defined the corresponding analytic function, see [14]. Here we further study the cardioid domain, to define and study starlike functions associated with cardioid domain. [ABSTRACT FROM AUTHOR]

We prove some combinatorial identities by an analytic method. We use the property that singular integrals of particular functions include binomial coefficients. In this paper, we prove combinatorial identities from the fact that two results of the particular function calculated as two ways using the residue theorem in the complex function theory are the same. These combinatorial identities are the generalization of a combinatorial identity that has been already obtained. [ABSTRACT FROM AUTHOR]

Our present investigation is motivated essentially by the fact that, in Geometric Function Theory, one can find many interesting and fruitful usages of a wide variety of special functions and special polynomials. The main purpose of this article is to make use of the (p, q)- Lucas polynomials Lp,q,n(x) and the generating function GLp, q, n (x) (z), in order to introduce three new subclasses of the bi-univalent function class Σ. For functions belonging to the defined classes, we then derive coefficient inequalities and the Fekete-Szego inequalities. Some interesting observations of the results presented here are also discussed. We also provide relevant connections of our results with those considered in earlier investigations. [ABSTRACT FROM AUTHOR]

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By this research notes, the well-known Tremblay operator and certain core knowledge therewith are firstly introduced and an extensive result containing numerous (analytic and) geometric properties (of possible applications of the related operator) along with a number of special implications are then constituted. As method for proving, the well-known assertion proposed by [8] is also considered there. [ABSTRACT FROM AUTHOR]

A new approach to modeling the geometric structure of real materials based on a new type of functions – porous functions – is introduced. The general concept, basic operations, operations of calculus, visualization and interpretations, and potential applications of porous functions are outlined. [ABSTRACT FROM AUTHOR]

For analytic functions f (z) = z + Σ∞k=2fkzk and g(z) = z + Σ∞k=2gkz k=2 k=2 in the unit disk properties of the Hadamard compositions Df [Sf * Dn [s]g and Dn [r] f * Dnl [R]g of their Gelfond-Leont'ev-Salagean derivatives Dnl,]f(z) =z+Σ∞k=2 (k) fkzk n and Gelfond-Leont'ev-Ruscheweyh derivatives Dln[R]f(z) = z + Σ∞k=2 fkZk ln+k -1 are investigated. For study, generalized orders are used. A connection between the growth of the maximal term of the Hadamard composition of Gelfond-Leont'ev-Saalaagean derivatives or Gelfond-Leont'ev-Ruscheweyh derivatives and the growth of the maximal term of these derivatives of Hadamard composition is established. Similar results are obtained in terms of the classical order and the lower order of the growth. [ABSTRACT FROM AUTHOR]

Structure and distribution of cells in histological images cause considerable variability among the tissue patterns and make the retrieving and classification as challenging tasks for this type of medical images. In this paper, we propose to extract four local features, namely local energetic information, local structural information, local geometric information, and local patterns to represent the huge texture variability of the histological images in a feature space. For extracting these features, the Riesz transform and Monogenic local binary patterns are used. Riesz transform is an extension of the Hilbert transform for 2-D signals. It provides a monogenic representation for an image where we can capture some local structure information. We used these local features for classification and retrieving purposes. We validated our proposed method on two multiclass archives of histological images, namely Kimiapath24 and Kather datasets. We achieved performance of more than 90% for classification and retrieval in two datasets. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the Schur geometric convexity of related function for Holders Inequality by using majorization inequality theory, giving a complete critical condition of Schur Geometrically convex function for Holders Inequality related function and some applications are established. [ABSTRACT FROM AUTHOR]

The study of operators plays an essential role in Mathematics, especially in Geometric Function Theory in Complex Analysis and its related fields. Many derivative and integral operators can be written in terms of convolution of certain analytic functions. The class of analytic functions, which has an essential place in the theory of geometric functions, has been studied by many researchers before. This topic still maintains its popularity today. In this paper, we investigate certain subclasses of analytic functions defined by generalized differential operators involving binomial series. Also, we obtain coefficient estimates involving of the nonhomogeneous Cauchy-Euler differential equation of order r. [ABSTRACT FROM AUTHOR]

In this paper, we derive some bounds for the real parts and arguments of the functionals given by ... where Js;b is the widely-investigated Srivastava-Attiya operator defined on the class of normalized analytic functions f in the open unit disk ... with suitable real parameters s and b. These results reduce upon specialization to some well-known inclusion relationships for several classes of functions with given geometric properties. We also make a comparison between one of the results obtained here and an already known result for some specific cases. [ABSTRACT FROM AUTHOR]

This work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to prove some useful properties of the subclass of slice regular functions, previously known only over quaternions. Firstly, they are applied to derive from the maximum modulus principle a version of the minimum modulus principle, which is in turn applied to prove the open mapping theorem. Secondly, they are applied to prove, in the context of the classification of singularities, the counterpart of the Casorati-Weierstrass theorem. [ABSTRACT FROM AUTHOR]

We consider the well-known problem of the geometric theory of functions of a complex variable on non-overlapping domains with free poles on radial systems. The main results of the present work strengthen and generalize several known results for this problem. [ABSTRACT FROM AUTHOR]

The present work is an attempt to give partial proofs of certain conjectures on the fifth coefficient of certain normalized analytic functions. Further, bounds on the sixth and seventh coefficients for the starlike functions related to a lune are also investigated. The non-sharp bound on third and fourth Hankel determinants are also obtained. [ABSTRACT FROM AUTHOR]

Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators, integral operators, and classes of analytic functions, especially the classes that are generated by convolution product (Hadamard product). In this effort, we aim to introduce a quantum symmetric conformable differential operator (Q-SCDO). This operator generalized some well-know differential operators such as Sàlàgean differential operator. By employing the Q-SCDO, we present subclasses of analytic functions to study some of its geometric solutions of q-Painlevé differential equation (type III). [ABSTRACT FROM AUTHOR]

Grunsky operators play an important role in classical geometric function theory and in the study of Teichmüller spaces. The Grunsky map is known to be holomorphic on the universal Teichmüller space. In this paper the authors deal with the compactness of a Grunsky differential operator. They will give upper and lower estimates of the essential norm of a Grunsky differential operator and discuss when a Grunsky differential operator is a p-Schatten class operator. [ABSTRACT FROM AUTHOR]

The principal goal of this paper is to extend the classical problem of finding the values of α ∈ ℂ for which either f ˆ α (z) = ∫ 0 z (f (ζ) ∕ ζ) α d ζ or f α (z) = ∫ 0 z (f ′ (ζ)) α d ζ are univalent, whenever f belongs to some subclasses of univalent mappings in D , to the case of harmonic mappings, by considering the shear construction introduced by Clunie and Sheil-Small in [4]. [ABSTRACT FROM AUTHOR]

Exploiting this article, we provide the coefficient estimate with m-th root transform for a class defined by Hohlov operator using quasi-subordination for conic domains. The authors sincerely hope this article will revive this concept and encourage the other researchers to work in this quasi subordination in the near future in the area of complex function theory. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study the properties of three dimensional Lorentzian concircular structure manifolds ((LCS)3-manifolds) endowed with almost h-conformal Ricci solitons. Also, we discuss the h-conformal gradient shrinking Ricci solitons on (LCS)3-manifolds. Finally, the examples of almost h-conformal Ricci soliton on an (LCS)3-manifold are provided in the region where (LCS)3-manifold is expanding. [ABSTRACT FROM AUTHOR]

In this note, an extensive result consisting of analytic functions will firstly be constituted and it will then be proven by means of the well-known assertions given in [12, 15]. As it was detailed in the works in [3, 5, 7, 16, 20], several special results concerning analytic and geometric properties of certain complex valued functions will also be created as some of related implications of the main result. Finally, for other possible implications pertaining to the results given by [4, 7, 9, 13, 24, 25], a large number of conclusions and recommendations will be pointed out in the last section. [ABSTRACT FROM AUTHOR]

In this paper we investigate the solutions of a class of (k+1)-order rational difference equations. We give conditions for the parameters ensuring that the considered equation has a unique positive equilibrium point that is locally asymptotically stable and every positive solution of the considered equation is bounded and increasing and converges to the unique positive equilibrium point. [ABSTRACT FROM AUTHOR]

Inequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel. [ABSTRACT FROM AUTHOR]

The concept of hyperelastic deformations of bi-conformal energy is developed as an extension of quasiconformality. These deformations are homeomorphisms h : X → onto Y between domains X , Y ⊂ R n of the Sobolev class W loc 1 , n (X , Y) whose inverse f = = def h - 1 : Y → onto X also belongs to W loc 1 , n (Y , X) . Thus the paper opens new topics in Geometric Function Theory (GFT) with connections to mathematical models of Nonlinear Elasticity (NE). In seeking differences and similarities with quasiconformal mappings we examine closely the modulus of continuity of deformations of bi-conformal energy. This leads us to a new characterization of quasiconformality. Specifically, it is observed that quasiconformal mappings behave locally at every point like radial stretchings; if a quasiconformal map h admits a function ϕ as its optimal modulus of continuity at a point x ∘ , then f = h - 1 admits the inverse function ψ = ϕ - 1 as its modulus of continuity at y ∘ = h (x ∘) . That is to say, a poor (possibly harmful) continuity of h at a given point x ∘ is always compensated by a better continuity of f at y ∘ , and vice versa. Such a gain/loss property, seemingly overlooked by many authors, is actually characteristic of quasiconformal mappings. It turns out that the elastic deformations of bi-conformal energy are very different in this respect. Unexpectedly, such a map may have the same optimal modulus of continuity as its inverse deformation. In line with Hooke's Law, when trying to restore the original shape of the body (by the inverse transformation), the modulus of continuity may neither be improved nor become worse. However, examples to confirm this phenomenon are far from being obvious; indeed, elaborate computations are on the way. We eventually hope that our examples will gain an interest in the materials science, particularly in mathematical models of hyperelasticity. [ABSTRACT FROM AUTHOR]

In this present investigation, by using the Horadam polynomials, we aim to build a bridge between the theory of geometric functions and that of special functions, which are usually considered very different fields. Thus, we introduce some new classes of bi-univalent functions defined by combining the q-derivative operator and the Horadam polynomials. Afterwards, we derive coefficient inequalities and consider the classical Fekete-Szegö problem. [ABSTRACT FROM AUTHOR]

In this paper, we present the best possible parameters α1, α2, α3 and β1, β2, β3 such that the double inequalities Cα1 (a; b)G1-α1 (a, b) < T(a, b) < Cβ1 (a, b)G1-β1 (a, b); α2C(a, b) + (1 - α2)G(a, b) < T(a, b) < β2C(a, b) + (1 - β2)G(a, b), α3/G(a, b)+1 - α3/C(a, b) < 1/T(a, b) < β3/G(a, b) + 1 - β3/C(a, b) hold for all a, b > 0 with a 6 = b, where G(a, b) = √ab, C(a, b) = (a² + b²) / (a+b) and T(a, b) = 2 ∫ π/20 √a2 cos2(t) + b² sin²(t)dt/π are the geometric, contraharmonic and Toader means of a and b, respectively. [ABSTRACT FROM AUTHOR]

We consider an open extremal problem in geometric function theory of complex variables on the maximum of the functional [ABSTRACT FROM AUTHOR]

Although much research (f. e. [1], [3], [5], [7-15]) has been devoted to the extremal problems of a geometric function theory associated with estimates of functionals defined on systems of non-overlapping domains, however, in the general case the problems remain unsolved. The paper describes the problem of finding the maximum of a functional. This problem is to find a maximum of the product of inner radii of mutually non-overlapping symmetric domains with respect to a unit circle and the inner radius in some positive certain degree of the domain with respect to zero and description of extreme configurations. The topic of the paper is devoted to the study of the problem of the classical direction of the geometric theory of complex variable functions, namely, the extremal problems for non-overlapping domains. [ABSTRACT FROM AUTHOR]

In the first part of this work we present several new geometric properties of analytic functions by applying the differential subordination. In addition, several results in the geometric functions theory pointed out. In the second part we find upper bounds for coefficients of functions in class B∑q,µ (β, λ, h) which is defined by fractional q-calculus operators. [ABSTRACT FROM AUTHOR]

We want to remark explicitly that, by using the Ln(x) functions (essentially linked to Lucas polynomials of the second kind), our methodology builds a bridge, to our knowledge not previously well known, between the Theory of Geometric Functions and that of Special Functions, which are usually considered as very different fields. Thus, also making use of the differential operator Ik p;q, we introduce a new class of analytic bi-univalent functions. Coefficient estimates, Fekete-Szego inequalities and several special consequences of the results are obtained. [ABSTRACT FROM AUTHOR]

In the present paper, by using the Lp,q,n(x) functions, our methodology intertwine to yield the Theory of Geometric Functions and that of Special Functions, which are usually considered as very different fields. Thus, we aim at introducing a new class of biunivalent functions defined through the (p, qJ-Lucas polynomials. Furthermore, we derive coefficient inequalities and obtain Fekete-Szego problem for this new function class. [ABSTRACT FROM AUTHOR]