Close-to-convex functions defined by fractional operator

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Tarih

2013

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Erişim Hakkı

info:eu-repo/semantics/openAccess

Araştırma projeleri

Organizasyon Birimleri

Dergi sayısı

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 exists?(Z) ? C, depending on f(z) with Re( f?(z)/??(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(?) the class of such functions. Various properties of this class of functions is alos studied.

Açıklama

Anahtar Kelimeler

Analytic function, Close-to-convex, Convex, Fractional calculus, Multivalent functions, Starlike, Subordination

Kaynak

Applied Mathematical Sciences

WoS Q Değeri

Scopus Q Değeri

N/A

Cilt

7

Sayı

53-56

Künye

Aydoğan, S. M., Kahramaner, Y. & Polatoğlu, Y. (2013). Close-to-convex functions defined by fractional operator. Applied Mathematical Sciences, 7(53-56), 2769-2775. doi:10.12988/ams.2013.13246