Abstract
The close-to-convex analogue of a starlike functions by means of generalized discrete probability distribution and Poisson distribution was considered. Some coefficient inequalities and their connection to classical Fekete-Szego theorem are obtained. Our results provide strong connection between Geometric Function Theory and Statistics.
Highlights
IntroductionKeywords and phrases: analytic, univalent, Poisson, discrete, distribution series, probability, Fekete-Szego, coefficient
Let A denote the class of analytic functions f in the unit disk E = {z : |z| < 1}
Analytic Univalent Functions Defined by Generalized Discrete Probability ... 171 where ak ≥ 0, for all k ∈ N
Summary
Keywords and phrases: analytic, univalent, Poisson, discrete, distribution series, probability, Fekete-Szego, coefficient. In [[1], [2], [7]] derivations of certain geometric properties were carried out to establish connections between Geometric Function Theory and Statistics by means of generalized discrete probability distribution. Analytic Univalent Functions Defined by Generalized Discrete Probability ... Our result is robust because obtaining sharp estimates for the coefficients represents a much more difficult problem most especially when to extend from starlikeness to close-to-convexity. To achieve this our method shall follow the pattern of that of Allu et al [10]. We define the close to convex analogue of the class Sμ∗ associated with generalized distribution as follows. It is clear that Sμ∗ ⊂ Kμ ⊂ A, where Kμ represents the natural close-to-convex analogue of Sμ∗
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
