Classes of close-to-convex Functions Defined using Beta Negative Binomial Distribution

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DOI: https://doi.org/10.28924/2291-8639-24-2026-206
Published: Jul 6, 2026
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Waleed Al-Rawashdeh, Fatima Tayfou, Classes of close-to-convex Functions Defined using Beta Negative Binomial Distribution, Int. J. Anal. Appl., 24 (2026), 206.

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Waleed Al-Rawashdeh, Fatima Tayfou

Abstract

In this paper, we make use of convolution of the power series whose coefficients are the beta negative binomial distribution probabilities and a power series of an analytic function in the unit disk \(\mathbb{D}\), to introduce a novel class of Ma-Minda type close-to-convex functions associated with the \(q\)-analogue of sine function. In addition, we find bounds for the growth and distortion of functions belonging to our class and some of its various subclasses. Moreover, we obtain the classical Fekete-Szegö inequality of functions belonging to our class and some of its various subclasses.

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