Subclasses of Bi-Univalent Functions Associated with q-Confluent Hypergeometric Distribution Based Upon the Horadam Polynomials

Sheza El-Deeb,Bassant El-Matary

doi:10.31197/atnaa.768591

Abstract

In this paper, we introduce new subclasses of analytic and bi-univalent functions connected with a q-confluent hypergeometric distribution by using the Horadam polynomials which, these polynomials, the families of orthogonal polynomials and other special polynomials, as well as their extensions and generalizations, are potentially important in a variety of disciplines in many branches of science, especially in the mathematical, statistical and physical sciences. For more information associated with these polynomials . Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients |a₂| and |a₃| for functions in these subclasses and obtain Fekete-Szegő problem for these subclasses.

Highlights

In [23] Srivastava presented and motivated about brief expository overview of the classical q-analysis versus the so-called (p, q)-analysis with an obviously redundant additional parameter p
The object of the present paper is to introduce new subclasses of the function class Σ involving the q−conuent Hypergeometric function connected with Horadam polynomials hn(x) that generalize the previous dened classes, and nd estimates on the coecients |a2|, and |a3| for functions in these new subclasses of the function class Σ
Let the function f given by (1) belongs to the class KΣλ,q ζ cos θeiθ, γ, b, c, m, x ,

Summary

Introduction

In [23] Srivastava presented and motivated about brief expository overview of the classical q-analysis versus the so-called (p, q)-analysis with an obviously redundant additional parameter p. The generating function of the Horadam polynomials hn(x) is given as follows (see [11])

Results

Conclusion