Bulletin of the
Korean Mathematical Society
BKMS

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

Article

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Bull. Korean Math. Soc. 2015; 52(6): 1805-1818

Printed November 30, 2015

https://doi.org/10.4134/BKMS.2015.52.6.1805

Copyright © The Korean Mathematical Society.

On certain generalized $q$-integral operators of analytic functions

Sunil Dutt Purohit and Kuppathai Appasamy Selvakumaran

Rajasthan Technical University, R. M. K College of Engg. and Technology

Abstract

In this article, we first consider a linear multiplier fractional $q$-differintegral operator and then use itto define new subclasses of $p$-valent analytic functions in the open unit disk $\mathcal{U}$. An attempt has also been made to obtain two new $q$-integral operators and study their sufficient conditions on some classes of analytic functions. We also point out that the operators and classes presented here, being of general character, are easily reducible to yield many diverse new and known operators and function classes.

Keywords: analytic functions, $q$-integral operators, fractional $q$-calculus operators, $p$-valently starlike and $p$-valently convex functions of complex order

MSC numbers: 30C45, 26A33