Coefficient properties for the subclasses of convex functions with respect to other points

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Subclasses of Bi-Univalent Functions Associated with Hohlov Operator

The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors

A Subclass of Quasi-Convex Functions with Respect to Symmetric Points

Abstract Let C s (A, B) denote the class of functions f which are analytic in an open unit disc D = {z : |z| &lt; 1} and satisfying the condition 2(zf (z)

A subclass of harmonic meromorphic functions

Complex-valued harmonic meromorphic functions that are univalent and orientation preserving outside the unit circle Ũ can be written in the form f = h + g, where h and g are analytic in Ũ. We define and investigate a subclass of harmonic meromorphic functions. We obtain coefficient conditions, extreme points, distortion bounds, convolution conditions and convex combinations for the above subclass of harmonic meromorphic functions

Second Hankel Determinant for Strongly Bi-Starlike of order α

Let A denote the class of functions f (z) = z + �∞ n=2 anz n which are analytic in the open unit disc U = {z : |z| < 1}. Let S denote the class of all functions in A that are univalent in U. A function f ∈ A is said to be bi-univalent in U if both f and f −1 are univalent in U. Let denote the class of bi-univalent functions in U. In this paper, we obtained the upper bounds for the second Hankel functional |a2a4 − a2 3 | for strongly bi-starlike of order α

Classes with Negative Coefficients and Convex with Respect to Other Points

Let S be the class of functions f which are analytic and univalent in the open unit disc D = {z : |z| < 1} given by f(z) = z + ∞ n=2 anzn and an a complex number. Let T denote the class consisting of functions f of the form f(z) = z − ∞ n=2 anzn where an is a non negative real number. In [8], Wong and Janteng introduced 3 subclasses of T ; CsT(α, β), CcT(α, β) and CscT(α, β), consisting of analytic functions with negative coefficients and are respectively convex with respect to symmetric points, convex with respect to conjugate points and convex with respect to symmetric conjugate points. Here, α and β are to satisfy certain constraints. This paper extends the result in [8] to other properties namely growth and extreme points

First order differential subordination associated with Cassini curve

Let p be an analytic function defined on the open unit disc with 01p. In this paper, we determine the conditions for such that certain subordination properties hold for pz is subjected to certain geometric conditions involving the expressions 1',zpz 1'/zpzpz and 21'/zpzpz of which each is subordinated to 1cz and the condition for is determined

Results on toeplitz determinants for subclasses of analytic functions associated to q-derivative operator

An analytic function, also known as a holomorphic function, is a complex-valued function that is differentiable at every point within a given domain. In other words, a function f (z) is analytic in a domain U if it has a derivative f ′ (z) at every point z in U. Let A represent the set of functions f that are analytic within the open unit disk D = {z ∈ ℂ : |z| < 1}. These functions possess a normalized Taylor-Maclaurin series expansion written in the form f (z) = z + Í∞ n=2 an z n where an ∈ ℂ, n = 2, 3, . . .. In recent years, the field of q-calculus has gained significant attention and research interest among mathematicians. The applications of this field are broadly applied in numerous subdivisions of physics and mathematics. In this research, we assume that S ∗ q and ℝq are subclasses of analytic functions obtained by applying the q-derivative operator. The objective of this paper is to obtain estimates for coefficient inequalities and Toeplitz determinants whose elements are the coefficients an for f ∈ S ∗ q and f ∈ Rq

Properties of harmonic functions which are starlike of complex order with repect to symmetric points

Let H denote the class of functions f which are harmonic, orientation preserving and univalent in the open unit disc D = {z : |z| < 1}. This paper defines and investigates a family of complex-valued harmonic functions that are orientation preserving and univalent in D and are related to the functions starlike of complex order with respect to symmetric points. The authors obtain extreme points, convolution and convex combination properties

Class with negative coefficients and convex with respect to symmetric points

Let C_s T(A,B) denote the class of functions f(z)=z-∑_(n=2)^∞ a_n z^n which are analytic in an open unit disc D={z:|z|<1} and satisfying the condition (2(zf^' (z))^')/((f(z)-f(-z))^' )≺(1+Az)/(1+Bz),-1≤B<A≤1,z∈D. The aims of paper are to determine coefficient estimates and distortion bounds for the class C_s T(A,B)