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

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.