Close-to-convex functions defined by fractional operator
Applied Mathematical Sciences, vol.7, no.53-56, pp.2769-2775, 2013 (Scopus)
- Publication Type: Article / Article
- Volume: 7 Issue: 53-56
- Publication Date: 2013
- Doi Number: 10.12988/ams.2013.13246
- Journal Name: Applied Mathematical Sciences
- Journal Indexes: Scopus
- Page Numbers: pp.2769-2775
- Keywords: Close-to-convex, Convex, Fractional calculus, Starlike
- Open Archive Collection: AVESIS Open Access Collection
- İstanbul Ticaret University Affiliated: Yes
Abstract
Let S denote the class of functions f(z) = z + a2z2+... analytic and univalent in the open unit disc D = {z ∈ C||z|<1}. Consider the subclass and S* of S, which are the classes ofconvex and starlike functions, respectively. In 1952, W. Kaplan introduced a class of analyticfunctions f(z), called close-to-convex functions, for which there existsφ(Z) ∈ C, depending on f(z) with Re( f′(z)/φ′(z) ) > 0 in , and prove that every close-to-convex function is univalent. The normalized class of close-to-convex functions denoted by K. These classesare related by the proper inclusions C ⊂ S* ⊂ K ⊂ S. In this paper, we generalize the close-to-convex functions and denote K(λ) the class of such functions. Various properties of this class of functions is alos studied.©2013 Melike Aydog̃an et al.