Coefficient estimates of certain subclasses of analytic functions associated with Hohlov operator

TL;DR

This paper introduces a new subclass of analytic functions using Hohlov's operator, derives sharp bounds for Fekete-Szeg"o problems and Hankel determinants, and connects these results with existing function classes.

Contribution

It defines the subclass r_{a,b}^{c}, finds sharp bounds for key functionals, and expresses extremal functions via hypergeometric functions, advancing geometric function theory.

Findings

Sharp bounds for Fekete-Szeg"o problems obtained.

Upper bounds for second and third Hankel determinants established.

Extremal functions expressed in terms of hypergeometric functions.

Abstract

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 linear operator due to Hohlov \cite{6}, a new subclass $\mathcal{R}_{a,b}^{c}$ of analytic functions defined in the open unit disk is introduced. For both real and complex parameter, the sharp bounds for the Fekete-Szeg\"{o} 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 $\mathcal{R}_{a,b}^{c}$ is derived. Relevant connections of the new results with well known ones are pointed out.