J. Patel

Classes of multivalent analytic functions involving the Dziok-Srivastava operator

The object of the present paper is to investigate some inclusion relationships and a number of other useful properties of several subclasses of multivalent analytic functions, which are defined here by using the Dziok-Srivastava operator. Relevant connections of the results presented here with those obtained in earlier works are pointed out.

Certain subclasses of multivalent functions associated with a family of linear operators

The main object of the present paper is to investigate a number of inclusion relationships and some other useful properties of several interesting subclasses of analytic and p-valent functions, which are defined here by means of a certain linear operator. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.

A certain class of p-valently analytic functions

The object of the present paper is to derive various properties and characteristics of certain subclasses of p-valently analytic functions in the open unit disk by using the techniques involving the Briot-Bouquet differential subordination. The results presented here not only improve and sharpen the earlier works but they also give rise to a number of new results for simpler function classes.

Certain properties of multivalent functions associated with an extended fractional differintegral operator

Abstract Let A k ( p ) denote the class of functions of the form f ( z ) = z p + ∑ n = k ∞ a p + n z p + n ( p , k ∈ N = { 1 , 2 , 3 , … } ) which are analytic in the open unit disk U = { z : z ∈ C and | z | 1 } . By making use of the techniques of the differential subordination, we derive certain properties of the extended fractional differintegral operator Ω z ( λ , p ) ( - ∞ λ p + 1 ; p ∈ N ) (introduced recently by Patel and Mishra) defined in the class A k ( p ) .

On certain sufficient conditions for close-to-convexity

In this paper, we derive certain sufficient conditions for close-to-convexity of analytic functions by using the techniques of differential subordinations. Relevant connections of the results presented here with those obtained in earlier works are pointed out.

Properties of a class of multivalent analytic functions

Abstract We introduce a certain general class ν p λ ( a , c , A , B ) of multivalent analytic functions in the open unit disc involving a linear operator. The object of the present is to investigate various properties and characteristics of this class by using the techniques of Briot-Bouquet differential subordination.

Argument estimates of certain multivalent functions involving a linear operator

The purpose of this paper is to derive some argument properties of certain multivalent functions in the open unit disk involving a linear operator. We also investigate their integral preserving property in a sector.

Properties of a class of analytic functions involving a linear operator

(1 .1) / ( ζ ) = ζ + Σ α η ζ η n=2 which are analytic in the open unit disc Ε = {ζ € C : \z\ < 1}. Let <S, S*(a) and K.(a) (0 < a < 1) denote the subclasses of functions in A which are respectively univalent, starlike of order α and convex of order a in E. We denote <S*(0) = S* and /C(0) = K. For given arbitrary numbers A, Β satisfying 1 < Β < A < 1, let P(A,B) be the class of functions of the form

Inclusion and Subordination Properties of Multivalent Analytic Functions Involving Cho-Kwon-Srivastava Operator

The object of the present paper is to derive some inclusion and subordination results for certain classes of multivalent analytic functions in the open unit disk, which are defined in terms of the Cho-Kwon-Srivastava operator. Some interesting corollaries are derived and the relevant connection of the results obtained in this paper with various known results are also pointed out.

On Certain Subclasses of Analytic Functions Involving Carlson-Shaffer Operator and Related to Lemniscate of Bernoulli

The object of the present investigation is to solve the Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a new class of analytic functions involving the Carlson-Shaffer operator in the unit disk. We also obtain a sufficient condition for normalized analytic functions in the unit disk to be in this class.