Starlikeness of functions in the range of a class of integral operators

Abstract

For β < 1, let 𝒫_β denote the class of normalized analytic functions whose derivatives have real part greater than β. Recently, Fournier and Ruscheweyh [5] Fournier, R. and Ruscheweyh, St. (1994). On two extremal problems related to univalent functions. Rocky Mountain J. Math., 24: 529–538. [Crossref], [Web of Science ®] [Google Scholar] developed a method for finding the best (least) bound β such that a certain integral operator V _λ maps the class 𝒫_β into the familiar class 𝒮* of starlike functions in the unit disk. The main object of this paper is to show how their method can be made more readily available for several other classes of integral operators.