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

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

On boundedness and compactness of a generalized Srivastava–Owa fractional derivative operator

AbstractThe purpose of this present effort is to define a new fractional differential operator Tzβ,τ,γ, involving Srivastava–Owa fractional derivative operator. Further, we investigate some geometric properties such as univalency, starlikeness, convexity for their normalization, we also study boundedness and compactness of analytic and univalent functions on weighted μ-Bloch space for this operator. The method in this study is based on the generalized hypergeometric function