Applications of the Bell Numbers on Univalent Functions Associated with Subordination

Sh Najafzadeh,Mugur Acu,Muhammad Arif

doi:10.1155/2022/2324774

Sh Najafzadeh, Mugur Acu + Show 1 more

Open Access

https://doi.org/10.1155/2022/2324774

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Abstract

The motivation of the present paper is to define a new subclass of univalent functions associated with the q-analogue of the exponential function and the well-known Bell numbers based on subordination structure. Furthermore, we estimate the coefficient bound and extreme points. Also, geometric properties such as convexity and convolution preserving concept are investigated.

Highlights

For a fixed nonnegative integer k, the Bell numbers Bk is the number of equivalent relations on a set with k elements or equivalently the number of possible disjoint partitions of a set with k elements into nonempty subsets. e function ez− 1 ∞ zk
Let A denote the class of all functions F which are analytic in the open unit disk, D {z ∈ C: |z| < 1}, (2)
See [13–15]. e Hadamard product for function F(z), given by (5) and G(z) z − 􏽐∞ k 2 bkzk denoted by F ∗ G, is defined by

Summary

Introduction

For a fixed nonnegative integer k, the Bell numbers Bk is the number of equivalent relations on a set with k elements or equivalently the number of possible disjoint partitions of a set with k elements into nonempty subsets. e function ez− 1 ∞ zkQ(z) e 􏽘 Bk k!, (1)k 0 involving the Bell numbers was considered by Kumar et al.[1], see [2, 3]. Let A denote the class of all functions F which are analytic in the open unit disk, D {z ∈ C: |z| < 1}, (2) S is the subclass of A consisting of all well-known univalent functions in D.

Results

Conclusion