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Yayın Close-to-convex functions defined by fractional operator(2013) Aydoğan, Seher Melike; Kahramaner, Yasemin; Polatoğlu, YaşarLet 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.Yayın Harmonic mappings for which co-analytic part is a close-to-convex function of order b(Springer International Publishing, 2015-01-16) Polatoğlu, Yaşar; Kahramaner, Yasemin; Aydoğan, Seher MelikeIn the present paper we investigate a class of harmonic mappings for which the second dilatation is a close-to-convex function of complex order b, b is an element of C/{0} (Lashin in Indian J. Pure Appl. Math. 34(7):1101-1108, 2003).
