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An upper bound to the nonlinear functional for certain subclasses of analytic functions associated with Hankel determinant

Department of Engineering Mathematics, Gitam Institute of Technology, Rushikonda, GITAM University, Visakhapatnam 530 045, Andhra Pradesh, India

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and

T. Ramreddy

Department of Mathematics, Kakatiya University, Vidyaranyapuri 506 009, Warangal Dt., Andhra Pradesh, India

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https://doi.org/10.1142/S1793557113500423Cited by:0 (Source: Crossref)

Abstract

The objective of this paper is to obtain an upper bound to the second Hankel determinant for the functions belonging to strongly starlike and convex functions of order α(0 < α ≤ 1). Further, we introduce a subclass of analytic functions and obtain the same coefficient inequality for the functions in this class, using Toeplitz determinants.

Keywords:

AMSC: 30C45, 30C50

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