Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions

Abstract

By using a certain linear operator defined by a Hadamard product or convolution, several interesting subclasses of analytic functions in the unit disk are introduced and studied systematically. The various results presented here include, for example, a number of coefficient estimates and distortion theorems for functions belonging to these subclasses, some interesting relationships between these subclasses, and a wide variety of characterization theorems involving a certain functional, some general functions of hypergeometric type, and operators of fractional calculus. Some of the coefficient estimates obtained here are fruitfully applied in the investigation of certain subclasses of analytic functions with fixed finitely many coefficients.

A subclass of harmonic functions with negative coefficients defined by Dziok-Srivastava operator

“…One may refer to Carlson and Shaffer [2], Dziok and Srivastava [4] and Srivastava and Owa [15] for more details concerning these operators (see also [1,11,12,13]). …”

A Class of Starlike Functions Defined by the Dziok-Srivastava Operator

“…For more details on these operators see [1], [2], [3], [8], [9], [12] and [16]. Recently, Kanas and Srivastava [6], Srivastava and Mishra [17] and Vijaya and Murugusundaramoorthy [19] defined subclasses of functions of U CV and SP making use of various operators .…”

Subordination and superordination results associated with the generalized hypergeometric function

“…Several interesting operators, which are special cases of the linear operator (1.8) have been widely studied by Dziok and Srivastava [13], Carlson and Shaffer [6], Ruscheweyh [26], Cho et al, [7][8][9], Choi et al, [11] and others (also see [15] and [32]). Making use of the principle of subordination various subordination theorems involving certain integral operators for analytic functions in U were investigated by Bulboacȃ [5] (see also [4]), Miller and Mocanu [19], Owa and Srivastava [24].…”