Subordination Involving Regular Coulomb Wave Functions

Abstract

The functions 1+z, ez, 1+Az, A∈(0,1] map the unit disc D to a domain which is symmetric about the x-axis. The Regular Coulomb wave function (RCWF) FL,η is a function involving two parameters L and η, and FL,η is symmetric about these. In this article, we derive conditions on the parameter L and η for which the normalized form fL of FL,η are subordinated by 1+z. We also consider the subordination by ez and 1+Az, A∈(0,1]. A few more subordination properties involving RCWF are discussed, which leads to the star-likeness of normalized Regular Coulomb wave functions.