Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2011; 48(1): 169-182

Printed January 1, 2011

https://doi.org/10.4134/BKMS.2011.48.1.169

Copyright © The Korean Mathematical Society.

Subclasses of $k$-uniformly convex and $k$-starlike functions defined by S\u{a}l\u{a}gean operator

Bilal \c{S}eker, Mugur Acu, and Sevtap S\"{u}mer Eker

Batman University, Str. Dr. I. Ratiu 5-7, Dicle University

Abstract

The main object of this paper is to introduce and investigate new subclasses of normalized analytic functions in the open unit disc $\mathbb{U}$, which generalize the familiar class of $k$-starlike functions. The various properties and characteristics for functions belonging to these classes derived here include (for example) coefficient inequalities, distortion theorems involving fractional calculus, extreme points, integral operators and integral means inequalities.

Keywords: S\u{a}l\u{a}gean operator, $k$-starlike, $k$-uniformly convex, coefficient inequalities, distortion inequalities, extreme points, integral means, fractional derivative, integral operators

MSC numbers: Primary 30C45