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JMB Journal of Microbiolog and Biotechnology

OPEN ACCESS eISSN 0454-8124
pISSN 1225-6951
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Original Article

Kyungpook Mathematical Journal 2006; 46(4): 543-552

Published online December 23, 2006

Copyright © Kyungpook Mathematical Journal.

On Certain Novel Subclasses of Analytic and Univalent Functions

Huseyin Irmak1, Santosh Bhaurao Joshi2

1Department of Mathematics Education, Faculty of Education, Bac{s}kent University, Bau{g}l{i}ca Campus, Tr-06530, Ankara, Turkey
2Department of Mathematics, Walchand College of Engineering, Sangli 416 415, Maharashtra, India

Abstract

The purpose of the present paper is to introduce two novel subclasses ${mathcal T}_{mu}(n,lambda,alpha)$ and ${mathcal H}_{mu}(n,lambda,alpha;kappa)$ of analytic and univalent functions with negative coefficients, involving Ruscheweyh derivative operator. The various results investigated in this paper include coefficient estimates, distortion inequalities, radii of close-to-convexity, starlikenes, and convexity for the functions belonging to the class ${mathcal T}_{mu}(n,lambda,alpha).$ These results are then appropriately applied to derive similar geometrical properties for the other class ${mathcal H}_{mu}(n,lambda,alpha;kappa)$ of analytic and univalent functions. Relevant connections of these results with those in several earlier investigations are briefly indicated.

Keywords: analytic functions, univalent functions, starlike functions, convex functions, close-to-convex functions, Ruscheweyh derivative, coefficient estimates, distortion inequalities, Non-homogenous (Cauchy-Euler) differential equation