A new comprehensive subclass of analytic bi-close-to-convex functions

Authors: SERAP BULUT

Abstract: In a very recent work, Şeker and Sümer Eker [On subclasses of bi-close-to-convex functions related to the odd-starlike functions. Palestine Journal of Mathematics 2017; 6: 215-221] defined two subclasses of analytic bi-close-to-convex functions related to the odd-starlike functions in the open unit disk $\mathbb{U}$. The main purpose of this paper is to generalize and improve the results of Şeker and Sümer Eker (in the aforementioned study) defining a comprehensive subclass of bi-close-to-convex functions. Also, we investigate the Fekete-Szegö type coefficient bounds for functions belonging to this new class.

Keywords: Analytic and univalent functions, bi-univalent functions, close-to-convex functions, starlike functions, subordination principle, Fekete-Szegö problem

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