Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2013; 28(1): 143-154

Printed January 31, 2013

https://doi.org/10.4134/CKMS.2013.28.1.143

Copyright © The Korean Mathematical Society.

A certain subclass of Janowski type functions associated with $k$-symmetric points

Ohsang Kwon and Youngjae Sim

Kyungsung University, Kyungsung University

Abstract

We introduce a subclass $\mathcal{S}_{s}^{(k)}(A,B)$ $(-1 \leq B < A \leq 1)$ of functions which are analytic in the open unit disk and close-to-convex with respect to $k$-symmetric points. We give some coefficient inequalities, integral representations and invariance properties of functions belonging to this class.

Keywords: close-to-convex functions, Janowski type, sakaguchi functions, $k$-symmetric points

MSC numbers: Primary 30C45, 30C50