Coefficient Estimates for a Family of Starlike Functions Endowed with Quasi Subordination on Conic Domain

Abstract

In 1999, for (0≤k∞), the concept of conic domain by defining k-uniform convex functions were introduced by Kanas and Wisniowska and then in 2000, they defined related k-starlike functions denoted by k−UCV and k−ST respectively. Motivated by their studies, in our work, we define the class of k-parabolic starlike functions, denoted k−SHm,q, by using quasi-subordination for m-fold symmetric analytic functions, making use of conic domain Ωk. We determine the coefficient bounds and estimate Fekete–Szegö functional by the help of m-th root transform and quasi subordination for functions belonging the class k−SHm,q.

Keywords

• analytic function
• subordination
• quasi-subordination
• <i>m</i>-fold symmetric
• Fekete–Szegö inequality