Generalizations of harmonic starlike functions defined by new generalized derivative operator with respect to symmetric points

Abstract

In this paper, we define the operator D_(λ_1,λ_2,l,d)^(m,q,s) [α_i,β_j], and applying this operator to the harmonic function. Using this operator we introduce a new class of complex-valued harmonic functions with respect to symmetric points. We obtain coefficient bounds, extreme points, distortion bounds, convex combinations, and inclusion results and closure under an integral operator for this family of harmonic univalent functions.