Characteristic Properties of the New Subclasses of Analytic Functions

Abstract

Abstract:In this study, we introduce and investigate two new subclasses of analytic functions in the open unit disk. The object of the present paper is to derive characteristic properties of the functions belonging to these classes. Further, several coefficient inequalities for the functions belonging to these classes are also given.

Some subclasses of analytic functions of complex order

“…The class T S * C(α, β) and various other subclasses of T were studied by Altintaş et al [2,3], Irmak et al [6], Altintaş [1], Mustafa [7], and Silverman [8].…”

On the Characteristic Properties for Subclasses of the Higher Derivative of Analytic Functions

“…By setting s=1 and d=0 , the following corollaries are obtained by Mustafa [11]. Moreover, by setting   0 in Corollaries 2.12 and 2.13, we obtain interesting results for the classes S * and C , respectively, obtained by Mustafa [11]. Corollary 2.14.…”

“…Also, Mustafa [10] presented the subclass K ( , ), , 0,1 , which is the speculation of the near curved capacities, called near arched, regarding a starlike capacity g(z) of order and type of analytic functions . In [10,11], Mustafa discovered adequate conditions for the boundaries of the standardized Wright capacities to be in the class K ( , ) . As of late, Panigrahi and Murugusundaramoorthy [12] presented another subclass which is denoted by .…”

“…Also, we will use S * C ,  S * C ,  . We note the following: [11]; S * C ( , ,1,1,0)  C( , ) studied by Mustafa [11];…”

“…The value of z on the real axis so that is real and letting z → 1 − , we obtain ∑ { } ( ) ( ) By setting s=1 and d=0  in Theorem 2.2, the accompanying culminations are acquired by Mustafa [11].…”