The Fekete-Szego Functional Associated with the Mth Root Transformation Using Conical Domains

Abstract

Let A be the class of analytic functions in the open unit disk U = {z is an element of C : |z| < 1} and let R-alpha(p) be an operator defined on A by R-alpha(p)= f(z) * z/(1-z)(2(1-alpha)). We say that a function f in A is in the class k-SP alpha p if R-alpha(p)(f) is a k-parabolic starlike function. We focus on the Fekete-Szego inequality associated with the m th root transformation using conical domains for this class.