Coefficient Inequality for Transforms of Starlike and Convex Functions with Respect to Symmetric Points

• Journal title : Kyungpook mathematical journal
• Volume 55, Issue 2,  2015, pp.429-438
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2015.55.2.429
Title & Authors
Coefficient Inequality for Transforms of Starlike and Convex Functions with Respect to Symmetric Points
KRISHNA, DEEKONDA VAMSHEE; VENKATESWARLU, BOLLINENI; RAMREDDY, THOUTREDDY;

Abstract
The objective of this paper is to obtain sharp upper bound for the second Hankel functional associated with the $\small{k^{th}}$ root transform $\small{[f(z^k)]^{\frac{1}{k}}}$ of normalized analytic function f(z) when it belongs to the class of starlike and convex functions with respect to symmetric points, defined on the open unit disc in the complex plane, using Toeplitz determinants.
Keywords
starlike and convex functions with respect to symmetric points;upper bound;second Hankel functional;positive real function;Toeplitz determinants;
Language
English
Cited by
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