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.
Highlights
Gao and Zhou [2] introduced the subclass Ks of close-to-convex analytic functions as follows: Definition 1
Let A denote the family of analytic functions∑ ∞ f (z) = z + anzn n=2 (1.1)in the open unit disk U = {z : z ∈ C and |z| < 1}
Goyal and Singh [4] defined the general subclass of close-to-convex functions by using the principle of subordination as follows: Definition 2
Summary
Gao and Zhou [2] introduced the subclass Ks of close-to-convex analytic functions as follows: Definition 1 Goyal and Singh [4] defined the general subclass of close-to-convex functions by using the principle of subordination (see [8]) as follows: Definition 2
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