Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47885120190101Ruscheweyh-Type Harmonic Functions Defined By $q$- Differential Operators79888121210.22034/kjm.2019.81212ENGangadharanMurugusundaramoorthyDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore - 632014, India.0000-0001-8285-6619Jay M.JahangiriMathematical Sciences, Kent State University, Kent, Ohio, U.S.A.Journal Article20180721A 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.http://www.kjm-math.org/article_81212_6cf18940b12156412dcfac780d5c4d20.pdf