Some Subordination Results of Multivalent Functions Defined by Integral Operator

Abstract

The object of the present paper is to give some subordination properties of integral operator ᏼ α which was studied by Jung in 1993.

SUBORDINATION PROPERTIES OF UNIVALENT FUNCTIONS INVOLVING A NEW CLASS OF OPERATORS Vol. 2(1) Jan 2014, No. 4, pp. 37-52 R.K. RAINA AND POONAM SHARMA

“…There are several results in literature giving the subordination properties for univalent (or multivalent) analytic functions involving various types of linear operators associated with the operations of integration as well as differentiation (both ordinary and fractional), see for instance [3], [4], [5], [6], [11], [15] - [22], [28], [31] and [32]. Due to the generalized nature of the class of operators defined by (5), our results (Theorems 1 to 5) would obviously include (in view of the special cases of (5) mentioned in Section 1) the known results pertaining to the univalent case of the results obtained earlier, for example, in [5], [6], [11], [15] - [18], [20], [28], [31] and [32].…”

“…Next, by applying Lemma 1 and known procedures as used, for instance, in the paper of Srivastava et al [31] (see also [18], [19], [20] and [28]), we establish the following result.…”

On second-order differential subordinations for a class of analytic functions defined by convolution

“…Recent years,Özkan [16],Özkan and Altntaş [17], Lupaş [9], and Lupaş [10] (also see [1,2]) investigated some applications and results of subordinations of analytic functions given by convolution. Also Bulut [6] used the same techniques by using Komatu integral operator.…”