SOME CLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH CONIC REGIONS

Abstract

The purpose of the present paper is to introduce and investigate the function classes $k$-${\cal SP}(\alpha,\beta)$ and $k$-${\cal UCV} (\alpha, \beta)$ of analytic functions associated with conic regions in the open unit disk $\mathbb{U}$, which generalize the function classes defined and studied in a series of earlier papers by Kanas et al. [11, 12, 13, 14]. In particular, we consider the extremal problems for each of the above-mentioned function classes. The Fekete-Szegö problem is also considered for functions in the class $k$-${\cal SP}(\alpha,\beta)$. Moreover, we investigate some mapping properties for each of the function classes $k$-${\cal SP}(\alpha, \beta)$ and $k$-${\cal UCV}(\alpha, \beta)$.