Fractional Integral of a Confluent Hypergeometric Function Applied to Defining a New Class of Analytic Functions

Abstract

The study on fractional integrals of confluent hypergeometric functions provides interesting subordination and superordination results and inspired the idea of using this operator to introduce a new class of analytic functions. Given the class of functions An=f∈HU:fz=z+an+1zn+1+…,z∈U written simply A when n=1, the newly introduced class involves functions f∈A considered in the study due to their special properties. The aim of this paper is to present the outcomes of the study performed on the new class, which include a coefficient inequality, a distortion theorem and extreme points of the class. The starlikeness and convexity properties of this class are also discussed, and partial sums of functions from the class are evaluated in order to obtain class boundary properties.

Keywords

• analytic function
• coefficient inequality
• partial sum
• starlike function
• convex function
• fractional integral