Recently the present authors established refined versions of Bohr's inequality in case bounded analytic functions. In this article, we state and prove a generalization these results. Here, consider image origin boundary unit disk under function question let distance between both play central role our theorems. Thereby extend Bohr for class quasi-subordinations which contains classes majorizatio...

In this lecture, we aim at presenting a certain linear operator which is defined by means of the Hadamard product (or convolution) with a generalized hypergeometric function and then investigating its various mapping as well as inclusion properties involving such subclasses of analytic and univalent functions as (for example) k-uniformly convex functions and k-starlike functions. Relevant conne...

For d > 0 let Dd = {z : |z| < d} with D1 = D and let ∂Dd denote the boundary of Dd. Let S be the standard class of analytic, univalent functions f on D, normalized by f(0) = 0 and f ′(0) = 1 and let K denote the wellknown class of convex functions in S. For 0 ≤ α < 1 let S∗(α) denote the subclass of S of starlike functions of order α, i.e., a function f ∈ S∗(α) if and only if f satisfies the co...

I. M. Milin proposed, in his 1971 paper, a system of inequalities for the logarithmic coefficients normalized univalent functions on unit disk complex plane. This is known as conjecture and implies Robertson which turn Bieberbach conjecture. In 1984, Louis de Branges settled long-standing by showing Recently, O. Roth proved an interesting sharp inequality based proof Branges. this following Rot...

We show that the univalent local actions of the complexification of a compact connected Lie group K on a weakly pseudoconvex space where K is acting holomorphically have a universal orbit convex weakly pseudoconvex complexification. We also show that if K is a torus, then every holomorphic action of K on a weakly pseudoconvex space extends to a univalent local action of KC.

In recent years, the study of Hankel determinants for various subclasses normalised univalent functions f∈S given by f(z)=z+∑n=2∞anzn D={z∈C:|z|<1} has produced many interesting results. The main focus interest been estimating second determinant form H2,2(f)=a2a4−a32. A non-sharp bound H2,2(f) when f∈K(α), α∈[0,1) consisting convex order α was found Krishna and Ramreddy (Hankel starlike alpha. ...

Let F denote the class of all functions univalent in the unit disk and convex in the direction of the real axis. In the paper we discuss the functions of the class F which are n-fold symmetric, where n is positive even integer. For the class of such functions we find the Koebe set as well as the covering set, i.e. T f2F f ðDÞ and S f2F f ðDÞ. Moreover, the Koebe constant and the covering consta...

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...

One of the most important problems in study geometric function theory is knowing how to obtain sharp bounds coefficients that appear Taylor–Maclaurin series univalent functions. In present investigation, our aim calculate some estimates involving for family convex functions with respect symmetric points and associated a hyperbolic tangent function. These include first four initial coefficients,...