Convolution properties for certain classes of multivalent functions

AbstractRecently N.E. Cho, O.S. Kwon and H.M. Srivastava [Nak Eun Cho, Oh Sang Kwon, H.M. Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl. 292 (2004) 470–483] have introduced the class Sa,cλ(η;p;h) of multivalent analytic functions and have given a number of results. This class has been defined by means of a special linear operator associated with the Gaussian hypergeometric function. In this paper we have extended some of the previous results and have given other properties of this class. We have made use of differential subordinations and properties of convolution in geometric function theory

Subclasses of Multivalent Meromorphic Functions with a Pole of Order p at the Origin

In this paper, we carry out a systematic study to discover the properties of a subclass of meromorphic starlike functions defined using the Mittag–Leffler three-parameter function. Differential operators involving special functions have been very useful in extracting information about the various properties of functions belonging to geometrically defined function classes. Here, we choose the Prabhakar function (or a three parameter Mittag–Leffler function) for our study, since it has several applications in science and engineering problems. To provide our study with more versatility, we define our class by employing a certain pseudo-starlike type analytic characterization quasi-subordinate to a more general function. We provide the conditions to obtain sufficient conditions for meromorphic starlikeness involving quasi-subordination. Our other main results include the solution to the Fekete–Szegő problem and inclusion relationships for functions belonging to the defined function classes. Several consequences of our main results are pointed out

Certain classes of multivalent functions with negative coefficients associated with a convolution structure

Making use of a convolution structure, we introduce a new class of analytic functions $mathbb{T}^{p}_{g}(lambda,alpha, beta, )$ defined in the open unit disc and investigate its various characteristics. Further we obtained distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity for functions belonging to the class $mathbb{T}^{p}_{g}(lambda,alpha, beta).

Argument estimates of certain classes of P-Valent meromorphic functions involving certain operator

In this paper, by making use of subordination , we investigate some inclusion relations and argument properties of certain classes of p-valent meromorphic functions involving certain operator

Inclusion Properties for Certain Subclasses of Uniformly P-Valent Analytic Functions Involving Linear Operator

In this paper, the authors study some inclusion results for new subclasses of b-uniformly -valent functions in the open unit disc defined by differ-integral operator and some results of certain integral operator are also obtained

New Criteria for Meromorphic Multivalent Alpha-Convex Functions

The aim of the present paper is to obtain sufficient condition for the class of meromorphic p-valent alpha convex functions of order ξ and then to study mapping properties of the newly defined integral operators. Many known results appeared as special consequences of our work