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ON THE FEKETE-SZEGÖ PROBLEM FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS

T. N. Shanmugam, Srikandan Sivasubramanian

Open publisher page 11 citations

Abstract

ABSTRACT. In this present investigation, the authors obtain Fekete-Szegö’s inequality for certain normalized analytic functions f(z) defined on the open unit disk for which zf ′ (z)+αz 2 f ′ ′ (z) (1−α)f(z)+αzf ′(z) (α ≥ 0) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by convolution are given. As a special case of this result, Fekete-Szegö’s inequality for a class of functions defined through fractional derivatives is obtained. The Motivation of this paper is to give a generalization of the Fekete-Szegö inequalities obtained by Srivastava and Mishra.

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What this paper is about

ABSTRACT. In this present investigation, the authors obtain Fekete-Szegö’s inequality for certain normalized analytic functions f(z) defined on the open unit disk for which zf ′ (z)+αz 2 f ′ ′ (z) (1−α)f(z)+αzf ′(z) (α ≥ 0) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by convolution are given. As a special case of this result, Fekete-Szegö’s inequality for a class of functions defined through fractional derivatives is obtained. The Motivation of this paper is to give a generalization of the Fekete-Szegö inequalities obtained by Srivastava and Mishra.

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Available abstract

ABSTRACT. In this present investigation, the authors obtain Fekete-Szegö’s inequality for certain normalized analytic functions f(z) defined on the open unit disk for which zf ′ (z)+αz 2 f ′ ′ (z) (1−α)f(z)+αzf ′(z) (α ≥ 0) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by convolution are given. As a special case of this result, Fekete-Szegö’s inequality for a class of functions defined through fractional derivatives is obtained. The Motivation of this paper is to give a generalization of the Fekete-Szegö inequalities obtained by Srivastava and Mishra.

Key concepts: Mathematics, Generalization, Convolution (computer science), Analytic function, Unit disk, Class (philosophy), Pure mathematics, Inequality

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