Close-to-convex functions defined by fractional operator

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Aydoğan S. M., Kahramaner Y., Polatog̃lu Y.

Applied Mathematical Sciences, cilt.7, sa.53-56, ss.2769-2775, 2013 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7 Sayı: 53-56
  • Basım Tarihi: 2013
  • Doi Numarası: 10.12988/ams.2013.13246
  • Dergi Adı: Applied Mathematical Sciences
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.2769-2775
  • Anahtar Kelimeler: Close-to-convex, Convex, Fractional calculus, Starlike
  • İstanbul Kültür Üniversitesi Adresli: Evet

Özet

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.