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In this note, we slightly generalize Theorem 2 in the paper by M. Tunç and point out that the assumption of Theorem 3 is not sufficient. A misuse of the term 'mean' is also discussed. [ABSTRACT FROM AUTHOR]

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-closeto- convex functions related to the odd-starlike functions in the open unit disk 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. [ABSTRACT FROM AUTHOR]

In the paper we discuss two functionals of the Fekete-Szegö type: Φf(µ) = a2a4 -- µ,a3² and ©/(µ) = a4 -- µa2a3 for an analytic function f (z) = z + a2z² + a3z³ + . . ., z € Δ, (Δ = {z € C : |z| < 1}) and a real number µ. We focus our research on the estimation of (µ)| and \©f (µ)|, while f is either in S* (the class of starlike functions) or in Κ (the class of convex functions). [ABSTRACT FROM AUTHOR]

Let Ap denote the class of functions of the form f (z) = zp+ap+1 zp+1+a p+2zp+2+…which are regular and p-valent in the open unit disc D = {z : |z| < 1}. Let Mp(α) be the subclass of Ap consisting of functions f(z) which satisfy Re (z f′ (z)/ f(z) < α, (z ε D) for some real α (α > 1). The aim of this paper is to give a representation theorem, a distortion theorem and a coefficient inequality for the class Mp(α). [ABSTRACT FROM AUTHOR]