# Ruscheweyh-Type Harmonic Functions Defined By $q$- Differential Operators

Document Type : Original Article

Authors

1 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore - 632014, India.

2 Mathematical Sciences, Kent State University, Kent, Ohio, U.S.A.

Abstract

A class of Ruscheweyh-type harmonic functions is defined, using $q$-differential operators and sufficient coefficient conditions for this class is determined. We then consider a subclass of the aforementioned class consisting of functions with real coefficients and obtain necessary and sufficient coefficient bounds, distortion theorem, extreme points, and convex combination conditions for such class. It is shown that the classes of functions considered in this paper contain various well-known as well as new classes of harmonic functions.

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