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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]

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]

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]

In this paper, we introduce and examine certain subclass Mq,Σ (φ, β) of analytic and bi-univalent functions on the open unit disk in the complex plane. Here, we give coefficient bound estimates, upper bound estimate for the second Hankel determinant and Fekete-Szegö inequality for the function belonging to this class. Some interesting special cases of the results obtained here are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we define a class of analytic functions F(β,λ) (H, α, δ, μ), satisfying the following subordinate condition associated with Chebyshev polynomials {α [ zG ′ (z) G(z) ]δ + (1 - α) [ zG ′ (z) G(z) ]μ [ 1 + zG ′′ (z) G ′ (z) ]1-μ } H (z, t), where G(z) = λβz2f ′′ (z) + (λ - β) zf ′ (z) + (1 - λ + β) f (z), 0 ≤ α ≤ 1, 1 ≤ δ ≤ 2, 0 ≤ μ ≤ 1, 0 ≤ β ≤ λ ≤ 1 and t ∈ (1 2, 1 ]. We obtain initial coefficients |a2| and |a3| for this subclass by means of Chebyshev polynomials expansions of analytic functions in D. Furthermore, we solve Fekete-Szegö problem for functions in this subclass. We also provide relevant connections of our results with those considered in earlier investigations. The results presented in this paper improve the earlier investigations. [ABSTRACT FROM AUTHOR]

In the paper, a theorem on approximation of a wide class of analytic functions by generalized shifts uT (s + if(t )) of an absolutely convergent Dirichlet series uT (s) which in the mean is close to the Riemann zetafunction is obtained. Here f(t) is a monotonically increasing differentiable function having a monotonic continuous derivative such that f(2t) max tt2t 1 f'(t) « t as t 8, and uT 8 and uT « T2 as T 8. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions defined in the open unit disc. We use the Faber polynomial expansions to find upper bounds for the nth (n ≥ 3) Taylor- Maclaurin coefficients |an| of functions belong to these new subclasses with aĸ = 0 for 2 ≤ ĸ ≤ n - 1, also we find non-sharp estimates on the first two coefficients |a2| and |a3|. The results, which are presented in this paper, would generalize those in related earlier works of several authors. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to investigate the starlikeness, convexity, and close-to-convexity of some partial sums of the generalized Koebe function. Furthermore, we give some special results related with special cases of c constant. The results, which are presented in this paper, would generalize those in related works of several earlier authors. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new subclasses of biunivalent functions analytic in the exterior of the unit disc. The bounds obtained for the zeroth, first and second coefficient improves upon earlier known results. The results are obtained by refining the well-known estimates for the initial coefficients of the Carth 'eodory functions. [ABSTRACT FROM AUTHOR]

Let A be a unital primitive C*-algebra. This paper studies the spectral theories of B-Weyl elements and B-Browder elements in A, including the spectral mapping theorem and a characterization of B-Weyl spectrum. In addition, we characterize the generalized Weyl's theorem and the generalized Browder's theorem for an element a A and f(a), where f is a complex-valued function analytic on a neighborhood of s(a). What's more, the perturbations of the generalized Weyl's theorem under the socle of A and quasinilpotent element are illustrated. [ABSTRACT FROM AUTHOR]

In this work, considering a new subclass of bi-univalent functions which are m-fold symmetric and analytic functions in the open unit disk, we determine estimates for the general Taylor-Maclaurin coefficient of the functions in this class. Furthermore, initial upper bounds of coefficients for m-fold symmetric, analytic and bi-univalent functions were found in this study. For this purpose, we used the Faber polynomial expansions. In certain cases, the coefficient bounds presented in this paper would generalize and improve some recent works in the literature. We hope that this paper will inspire future researchers in applying our approach to other related problems. [ABSTRACT FROM AUTHOR]

The main objective of the present paper is to give with using the linear operator theory and also hypergeometric representations of related functions a new special subclass T Sp(2-r, 2-1), r ∈ Z+ of uniformly convex functions and in addition a suitable subclass of starlike functions with negative Taylor coefficients. Furthermore, the provided trailblazer outcomes in presented study are generalized to certain functions classes with fixed finitely many Taylor coefficients. [ABSTRACT FROM AUTHOR]

Let T be the class of analytic functions in the open unit disc U with f(0) = 0 and f ′ (0) = 1. For f(z) ∈ T, the Alexander integral operator A-1f(z), the Libera integral operator L-1f(z) and the Bernardi integral operator B-1f(z) were considered before. Using A-1f(z) and L-1f(z), a new integral operator Fλf(z) is considered. After discuss some properties of dominant for Fλf(z), another new integral operator O-1f(z) of f(z) ∈ T is discussed. The object of the present paper is to discuss the dominant of new integral operators Fλf(z) and O-1f(z) concerning with some starlike functions and convex functions in U. [ABSTRACT FROM AUTHOR]

In this paper, we introduce q-analogue of Liu-Owa integral operator and define a subclass of k-uniformly multivalent starlike functions of order γ, (0 ≤ γ < p; p ∈ N) by using the Liu-Owa q-integral operator. We examine coefficient estimates, growth and distortion bounds for the functions belonging to the subclass of k-uniformly multivalent starlike functions of order γ. Moreover, we determine radii of k-uniformly starlikeness, convexity and close-to-convexity for the functions belonging to this subclass. [ABSTRACT FROM AUTHOR]

In this extensive note, various differential-type operators in certain domains of the complex plane will be first introduced, a number of their comprehensive characteristic properties will be next pointed out and an extensive theorem dealing with some argument properties for several multivalent(ly) analytic functions will be also presented. In addition, numerous implications and suggestions, which can be obtained with the help of general result, will be determined. [ABSTRACT FROM AUTHOR]

For analytic functions f(z) in the class An, fractional calculus (fractional integrals and fractional derivatives) Dzλf (z) of order λ are introduced. Applying Dzλf (z) for f(z) ∈ An, we introduce the interesting subclass An (αm, β, ρ, λ) of An. The object of this paper is to discuss some properties of f (z) concerning Dzλf(z). [ABSTRACT FROM AUTHOR]

In this paper, we investigate the coefficient bound estimates, second Hankel determinant, and Fekete-Szegö inequality for the analytic bi-univalent function class, which we call Mocanu type bi-starlike functions, related to a shell-shaped region in the open unit disk in the complex plane. Some interesting special cases of the results are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, the authors investigate the initial coefficient bounds for a new generalized subclass of analytic functions related to Sigmoid functions. Also, the relevant connections with the famous classical Fekete-Szegö inequality for these classes are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the q-analogue of a certain family of linear operators in geometric function theory. Our main purpose is to define some subclasses of analytic functions by means of the q-analogue of linear operators and investigate various inclusion relationships with integral preserving properties. [ABSTRACT FROM AUTHOR]

Using (p,q) -Lucas polynomials and bi-Bazilevič functions, type functions of order p + iξ, we defined a new subclass of biunivalent functions. We obtained coefficient inequalities for functions belonging to the new subclass. In addition to these results, the upper bound for the Fekete-Szegö functional was obtained. Finally, for some special values of parameters, several corollaries were presented. [ABSTRACT FROM AUTHOR]

In this paper we deal with the radii of starlikeness and convexity of the q -Mittag-Leffler function for three different kinds of normalization by making use of their Hadamard factorization in such a way that the resulting functions are analytic in the unit disk of the complex plane. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays a pivotal role in this investigation. [ABSTRACT FROM AUTHOR]

In recent years, applications of Bessel differential equations have been commonly used in univalent functions theory. The main object of the present paper is to give some characteristic properties for some subclasses of uniformly starlike and convex functions which are defined here by means of the normalized form of the generalized Bessel function to be univalent in the open unit disc. Furthermore, we also establish some results of these subclasses related to a particular integral operator. Some corresponding consequences of our main results are also considered. [ABSTRACT FROM AUTHOR]

Motivated by the Rønning-starlike class [Proceedings of the American Mathematical Society 1993; 118: 189-196], we introduce the new class S*c that includes analytic and normalized functions f, which satisfy the inequality Re ... In this paper, we first give some examples that belong to the class S*c. Also, we show that if f ∈ S*c then Re{f(z)/z} > 1/2 in |z| < 1 (Marx-Strohhäcker problem). Afterwards, upper and lower bounds for |f(z)| are obtained where f belongs to the class S*c. We also prove that if f ∈ S*c and α ∈ [0, 1), then f is starlike of order α in the disc |z| < (1 - α)/(2 - α). At the end, we estimate logarithmic coefficients, the initial coefficients, and the Fekete-Szegö problem for functions f ∈ S*c. [ABSTRACT FROM AUTHOR]

Let S*(qc) denote the class of functions f analytic in the open unit disc Δ, normalized by the condition f(0) = 0 = f'(0) - 1 and satisfying the following inequality |(zf'(z)/f(z))² -1 | < c (z ∈ Δ, 0 < c ≤ 1). By use of the subordination principle for the univalent functions we have f ∈ S*(qc) ⇔ zf'(z)/f(z) ... √1 + cz (z ∈ Δ, 0 < c ≤ 1). In the present paper, for an analytic function p in Δ with p(0) = 1 we give some conditions which imply p(z) ... √1 + cz . These conditions are then used to obtain some corollaries for certain subclasses of analytic functions. [ABSTRACT FROM AUTHOR]

The main object of the present paper is to investigate convolution properties for a new subfamily of analytic functions that are defined by q -analogue of Ruscheweyh differential operator. Several consequences of the main results are also given. [ABSTRACT FROM AUTHOR]

In a recent work, Orhan et al. (Afrika Matematika, 2016) defined a subclass of analytic bi-univalent one-fold symmetric functions. The main purpose of this paper is to generalize and improve the results of Orhan et al. [ABSTRACT FROM AUTHOR]

In a very recent work, Şeker and Sümer Eker [On subclasses of bi-close-to-convex functions related to the odd-starlike functions. Palestine Journal of Mathematics 2017; 6: 215-221] defined two subclasses of analytic bi-closeto- convex functions related to the odd-starlike functions in the open unit disk U. The main purpose of this paper is to generalize and improve the results of Şeker and Sümer Eker (in the aforementioned study) defining a comprehensive subclass of bi-close-to-convex functions. Also, we investigate the Fekete-Szegö type coefficient bounds for functions belonging to this new class. [ABSTRACT FROM AUTHOR]

Given a domain Ω in the complex plane C and a univalent function q defined in an open unit disk D with nice boundary behaviour, Miller and Mocanu studied the class of admissible functions Ψ(Ω,q) so that the differential subordination ψ(p(z),zp′(z), z²p"(z); z) < h(z) implies p(z) < q(z), where p is an analytic function in D with p(0) = 1, : C³→ D! C and Ω = h(D). This paper investigates the properties of this class for q(z) = ez. As application, several sufficient conditions for normalized analytic functions f to be in the subclass of star-like functions associated with the exponential function are obtained. [ABSTRACT FROM AUTHOR]

In a very recent work, Şeker [Seker B. On a new subclass of bi-univalent functions defined by using Salagean operator. Turkish Journal of Mathematics 2018; 42: 2891-2896] defined two subclasses of analytic bi-univalent functions by means of Sălăgean differential operator and he obtained the initial Taylor-Maclaurin coefficient estimates for functions belonging to these classes. The main purpose of this paper is to improve the results obtained by Şeker in the aforementioned study. For this purpose, we define a general subclass of bi-univalent functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate an analytic function class Pq( λ, A, B) that we call the class of q-starlike and q-convex functions with respect to the parameter λ. We give coefficient bounds estimates, distortion bound and growth theorems for the functions belonging to this class. [ABSTRACT FROM AUTHOR]

Let (βn)n≥2 be a sequence of nonnegative real numbers and δ be a positive real number. We introduce the subclass A(βn, δ) of analytic functions, with the property that the Taylor coefficients of the function f satisfies Σ∞n≥2βn︱an︱≤ δ, where f(z) = z + Σ∞n=2 anzn . The class A(βn, δ) contains nonunivalent functions for some choices of (βn)n≥2 . In this paper, we provide some general properties of functions belonging to the class A(βn, δ), such as the radii of univalence, distortion theorem, and invariant property. Furthermore, we derive the best approximation of an analytic function in such class by using the semiinfinite quadratic programming. Applying our results, we recover some known results on subclasses related to coefficient inequality. Some applications to starlike and convex functions of order α are also mentioned. [ABSTRACT FROM AUTHOR]

Let A(n) be the class of functions f (z) = anzn + an+1zn+1 + ... (n ∈ ℕ), which are analytic in the open unit disk 핌, where an ≠ 0. For f (z) ∈ A(n), Miller and Mocanu in 1978 showed a very interesting result for f (z). Applying the result due to Miller and Mocanu, we would like to consider some new results for such functions. Our results in this paper are generalizations for results by Nunokawa in 1992. [ABSTRACT FROM AUTHOR]

Let X and Y be complex Banach spaces and 픻 be the open unit disc in the complex plane ℂ. Let φ be an analytic self-map of D and ℂ be an analytic operator-valued function from D into the space of all bounded linear operators from X to Y. The weighted composition operator : Wψ,φ: H(픻,X) → (픻, Y) is defined by Wψ,φ (f)(z) = ψ(z)(f (φ(z))), (z ∈ 픻,f ∈ H(픻,X)), where H(픻,X) is the space of all analytic X-valued functions on 픻. In this paper we provide necessary and sufficient conditions for the boundedness and compactness of weighted composition operators Wψ,φ between vector-valued Bloch- type spaces Bα(X) and Bβ(Y) for α, β > 0 in terms of ψ,φ, their derivatives, and the nth power φn of φ. [ABSTRACT FROM AUTHOR]

In this paper, we will discuss a newly constructed subclass of bi-starlike functions. Furthermore, we establish bounds for the coefficients and get the second Hankel determinant for the class SΣ(α, β). [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of estimating |a4 -a2a3|, where ak are the coefficients of a given close-to-convex function. The bounds of this expression for various classes of analytic functions have been applied to estimate the third Hankel determinant H3(1) . The results for two subclasses of the class C of all close-to-convex functions are sharp. This bound is equal to 2. It is conjectured that this number is also the exact bound of |a4 -a2a3| for the whole class C. [ABSTRACT FROM AUTHOR]

A typical problem in the theory of analytic functions is to study a functional made up of combinations of coefficients of the original function. Usually, there is a parameter over which the extremal value of the functional is needed. One of the important functionals of this type is the Fekete-Szegö functional defined on the class of analytic functions. In this paper we transfer the Fekete-Szegö problem to some classes of meromorphic functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and necessary and sufficient, conditions for the functions belonging to these classes, respectively, are also given. Furthermore, various properties like order of starlikeness and radius of convexity of the subclasses of these classes and radii of starlikeness and convexity of these subclasses are examined. [ABSTRACT FROM AUTHOR]

In this paper, the authors study some subordination and superordination properties for classes of p-valent meromorphic, analytic, and univalent functions associated with a linear operator ... (a, c, μ) of the Erdélyi-Kober type. Connections with several earlier results are also pointed out. [ABSTRACT FROM AUTHOR]

The main object of this scientific work is firstly to introduce various operators of fractional calculus (that is that fractional integral and fractional derivative(s)) in certain domains of the complex plane, then to determine certain results correlating with normalized analytic functions, which are analytic in certain domains in the complex plane, as a few applications of those operators, and also to present a number of extensive implications of them as special results. [ABSTRACT FROM AUTHOR]

Recently, in the literature, we can see quite a few papers about general coefficient bounds for subclasses of bi-univalent functions. However, we can find just a few papers about general coefficient estimates for subclasses of bi-close-to-convex functions. In the present study, we give and look into a new subclass of analytic and bi-close-to-convex functions in the open unit disk. Making use of the Faber series, we have an upper bound for the general coefficient of functions in this class. We also demonstrate the invisible behavior of the beginning coefficients of a special subclass of bi-close-to-convex functions. [ABSTRACT FROM AUTHOR]

An n-tuple of commuting operators, (T1,T2, , ...,Tn) on a Hilbert space H is said to be hypercyclic, if there exists a vector x ∈ H such that the set {T1 k1T2k2 ...T n ≥ 0, i =1, 2, ...n} is dense in H. In this paper, we give sufficient conditions under which the adjoint of an n-tuple of a weighted composition operator on a Hilbert space of analytic functions is hypercyclic. [ABSTRACT FROM AUTHOR]k n x : k i ≥ 0, i =1, 2, ...n} is dense in H. In this paper, we give sufficient conditions under which the adjoint of an n-tuple of a weighted composition operator on a Hilbert space of analytic functions is hypercyclic. [ABSTRACT FROM AUTHOR]

In this paper we find the exact orders of approximation of analytic functions by the complex versions of several potentials (including the Flett potential) generated by the Gamma function and by some singular integrals. [ABSTRACT FROM AUTHOR]

E. M. Patterson and K. Yano studied vertical and complete lifts of tensor fields and connections from a manifold Mn to its cotangent bundle T*(Mn). Afterwards, K. Yano studied the behavior on the cross-section of the lifts of tensor fields and connections on a manifold Mn to T*(Mn) and proved that when φ defines an integrable almost complex structure on Mn, its complete lift Cφ is a complex structure. The main result of the present paper is the following theorem: Let φ be an almost complex structure on a Riemannian manifold Mn. Then the complete lift Cφ of φ, when restricted to the cross-section determined by an almost analytic 1-form ω on Mn, is an almost complex structure. [ABSTRACT FROM AUTHOR]

The concept of differential subordination was introduced in [3] by S.S. Miller and P.T. Mocanu and the concept of strong differential subordination was introduced in [1], [2] by J.A. Antonino and S. Romaguera. In [5] we have studied the strong differential subordinations in the general case and in [6] we have studied the first order linear strong differential subordinations. In this paper we study the second order linear strong differential subordinations. Our results may be applied to deduce sufficient conditions for univalence in the unit disc, such as starlikeness, convexity, alpha-convexity, close-to-convexity respectively. [ABSTRACT FROM AUTHOR]

The concept of differential subordination was introduced in [4] by S. S. Miller and P. T. Mocanu and the concept of strong differential subordination was introduced in [1] by J. A. Antonino and S. Romaguera. This last concept was applied in the special case of Briot-Bouquet strong differential subordination. In this paper we study the strong differential subordinations in the general case, following the general theory of differential subordinations presented in [4]. [ABSTRACT FROM AUTHOR]

In the present paper we shall give the radius of starlikeness for the classes of p-valent analytic functions in the unit disc D = {z ||z| lt; 1}. [ABSTRACT FROM AUTHOR]

In the present paper, we obtain the upper bounds for the second Hankel determinant for certain subclasses of analytic and bi-univalent functions. Moreover, several interesting applications of the results presented here are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class Kαof all functions f univalent in the unit disk Δ that are normalized by f(0) = f' (0) - 1 = 0 while the sets f(Δ) are convex in two symmetric directions: eiαπ/2 and e -iαπ/2, α ∈ [0, 1] . It means that the intersection of f(Δ) with each straight line having the direction eiαπ/2 or e-iαπ/2 is either a compact set or an empty set. We find the Koebe set for Kα. Moreover, we perform the same operation for functions in Kβ,γ, i.e. for functions that are convex in two fixed directions: eiβπ/2 and eiγπ/2, -1 ≤ β ≤ γ γ ≤ 1. [ABSTRACT FROM AUTHOR]

In this work, we introduce and investigate two new subclasses of the bi-univalent functions in which both f and f -1 are m-fold symmetric analytic functions. For functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for ∣am+1∣ and ∣a2m+1∣. [ABSTRACT FROM AUTHOR]

In this study, we introduce and examine a subclasses of analytic and univalent functions defined by q - derivative. Here, we give necessary conditions for the functions to belong to these subclasses, and distortion bound and growth theorems for the functions belonging to these classes. [ABSTRACT FROM AUTHOR]