Coefficient Bounds for Subfamilies of Analytic Mappings of Complex Order Associated with the Ruscheweyh Derivative and Differential Equation

Year 2025, Volume: 17 Issue: 1, 120 - 135, 30.06.2025

Manzoor Hussain

https://doi.org/10.47000/tjmcs.1545173

Abstract

In this article, we introduced some new subfamilies of analytic mappings of complex order defined
by using the Ruscheweyh derivative and a family of non-homogenous Cauchy-Euler differential equations. We estimated the nth coefficient bounds and Fekete-Szeg¨o-type functional for functions in these subfamilies. The obtained results were then used in estimation of upper bounds on coefficients of logarithmic, bi-univalent, and second Hankel determinant for such functions. Various useful deductions relevant to recent results in the literature were made with some refinements of known results.

Keywords

Coefficient bounds , Fekete-Szegö inequalities , Ruscheweyh derivative , complex order , Cauchy--Euler differential equation

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