Differential subordination and superordination for certain subclasses of p-valent functions

In this paper, we study applications of the differential subordination and superordination of analytic p-valent functions in the open unit disc associated with certain operator defined by the Wright generalized hypergeometric function. Sandwich-type result involving this operator is also derived

Differential Subordination And Superordination For Analytic And Meromorphic Functions Defined By Linear Operators [QA331. N219 2007 f rb].

Suatu fungsi f yang tertakrif pada cakera unit terbuka U dalam satah kompleks C disebut univalen jika fungsi tersebut memetakan titik berlainan dalam U ke titik berlainan dalam C. A function f defined on the open unit disk U of the complex plane C is univalent if it maps different points of U to different points of C

Fractional calculus operator and its applications to certain classes of analytic functions. A study on fractional derivative operator in analytic and multivalent functions.

The main object of this thesis is to obtain numerous applications of fractional derivative operator concerning analytic and -valent (or multivalent) functions in the open unit disk by introducing new classes and deriving new properties. Our finding will provide interesting new results and indicate extensions of a number of known results. In this thesis we investigate a wide class of problems. First, by making use of certain fractional derivative operator, we define various new classes of -valent functions with negative coefficients in the open unit disk such as classes of -valent starlike functions involving results of (Owa, 1985a), classes of -valent starlike and convex functions involving the Hadamard product (or convolution) and classes of -uniformly -valent starlike and convex functions, in obtaining, coefficient estimates, distortion properties, extreme points, closure theorems, modified Hadmard products and inclusion properties. Also, we obtain radii of convexity, starlikeness and close-to-convexity for functions belonging to those classes. Moreover, we derive several new sufficient conditions for starlikeness and convexity of the fractional derivative operator by using certain results of (Owa, 1985a), convolution, Jack¿s lemma and Nunokakawa¿ Lemma. In addition, we obtain coefficient bounds for the functional of functions belonging to certain classes of -valent functions of complex order which generalized the concepts of starlike, Bazilevi¿ and non-Bazilevi¿ functions. We use the method of differential subordination and superordination for analytic functions in the open unit disk in order to derive various new subordination, superordination and sandwich results involving the fractional derivative operator. Finally, we obtain some new strong differential subordination, superordination, sandwich results for -valent functions associated with the fractional derivative operator by investigating appropriate classes of admissible functions. First order linear strong differential subordination properties are studied. Further results including strong differential subordination and superordination based on the fact that the coefficients of the functions associated with the fractional derivative operator are not constants but complex-valued functions are also studied

Differential Sandwich Theorems for p-valent Analytic Functions Defined by Cho–Kwon–Srivastava Operator

By using of Cho–Kwon–Srivastava operator, we obtain some subordinations and superordinations results for certain normalized p-valent an­alytic functions

New Developments in Geometric Function Theory

The book contains papers published in a Special Issue of Axioms, entitled "New Developments in Geometric Function Theory". An Editorial describes the 14 papers devoted to the study of complex-valued functions which present new outcomes related to special classes of univalent and bi-univalent functions, new operators and special functions associated with differential subordination and superordination theories, fractional calculus, and certain applications in geometric function theory

Subordination and superordination of certain linear operator on meromorphic functions

Using the methods of differential subordination and superordination, sufficient conditions are determined on the differential linear operator of meromorphic functions in the punctured unit disk to obtain, respectively, the best dominant and the best subordinant. New sandwich-type results are also obtained

Third Order Differential Subordination for Analytic Functions Involving Convolution Operator

في هذا البحث, من خلال استخدام المؤثر المعمم الجديد تم الحصول بعض نتائج التابعية التفاضلية من الدرجة الثالثة ونتائج التابعية التفاضلية العليا  للدوال التحليلية .كذلك تم تقديم بعض نظريات من نوع الساندوج .       In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented