Close-to-convex functions defined by fractional operator
Yükleniyor...
Dosyalar
Tarih
2013
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Erişim Hakkı
info:eu-repo/semantics/openAccess
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.
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
