Close-to-convex functions defined by fractional operator
Küçük Resim Yok
Tarih
2013
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Erişim Hakkı
info:eu-repo/semantics/closedAccess
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.©2013 Melike Aydog?an et al.
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.©2013 Melike Aydog?an et al.
Açıklama
Anahtar Kelimeler
Close-to-convex, Convex, Fractional calculus, Starlike
Kaynak
Applied Mathematical Sciences
WoS Q Değeri
Scopus Q Değeri
N/A
Cilt
7
Sayı
53-56
