Some New Results of Differential Subordinations for HigherOrder Derivatives of Multivalent Functions

Abstract

The main purpose of this paper is to study the differential subordination result for multivalent analytic functions. We give some applications of higher-order differential subordination results involving Hadamard product for multivalent analytic functions with generalized hypergeometric function in open unit disk. We have also discussed and studied a new class of higher-order derivatives of multivalent analytic functions in open unit disk of complex plane related to linear operator and we obtain some results connected inclusion relationship, argument estimate, integral representation and subordination property. by using the method of differential subordination we aim to prove some classical results in multivalent functions theory. We obtain some interesting properties of this class and establish several strong differential subordination for higher-order derivatives of multivalent analytic functions. By making use of the principle of subordination, we introduce a new class W_(p, q)^(l, k) (η,α_1, m; h) for higher-order derivatives of multivalent analytic functions associated with Dziok-Srivastava operator. We obtain some result for this class.