General Integral Operator of Analytic Functions Involving Functions with Positive Real Part

B A Frasin

doi:10.1155/2013/260127

Abstract

Let be the integral operator defined by where each of the functions and are, respectively, analytic functions and functions with positive real part defined in the open unit disk for all . The object of this paper is to obtain several univalence conditions for this integral operator. Our main results contain some interesting corollaries as special cases.

Highlights

Where each of the functions ffii and ppii are, respectively, analytic functions and functions with positive real part de ned in the open unit disk for all ii = 1, ... , nn. e object of this paper is to obtain several univalence conditions for this integral operator
Our main results contain some interesting corollaries as special cases
If h ∈ AA satis es zzzzz ββββ for all zz z zz, the integral operator FFββ(zz) de ned by (8) is in the class SS

Summary

Introduction

BBββ be the integral operator de ned by We obtain new sufficient conditions for the univalence of the general integral operator BBββ(zz) de ned by zz nn ttββ−1󵠉󵠉 Note that the integral operator BBββ generalizes the following operators introduced and studied by several authors: (1) If we let ζζii = 0, for all ii = 1, ...

Results

Conclusion