The main purpose of this paper, is to characterize new admissible classes of linear operator in terms of seven-parameter Mittag-Leffler function, and discuss sufficient conditions in order to achieve certain third-order differential subordination and superordination results. In addition, some linked sandwich theorems involving these classes had been obtained.  

In this paper, a new seven-parameter Mittag-Leffler function of a single com-plex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.

       In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.

    In this article, we introduce and study two new families of analytic functions by using strong differential subordinations and superordinations associated with Wanas differential operator/. We also give and establish some important properties of these families.

       Th  goal of the pr s nt p p r is to obt in some differ tial sub rdin tion an  sup r dination the rems for univalent functions related b  differential operator  Also, we discussed some sandwich-type results.

The concern of this article is the calculation of an upper bound of second Hankel determinant for the subclasses of functions defined by Al-Oboudi differential operator in the unit disc. To study special cases of the results of this article, we give particular values to the parameters A, B and λ

    In this paper, we derive some subordination and superordination results for certain subclasses of p− valent analytic functions that defined by generalized Fox-wright functions using the principle of differential subordination, ----------producing best dominant univalent solutions. We have also derived inclusion relations and solved majorization problem.

New speaker identification test’s feature, extracted from the differentiated form of the wave file, is presented. Differentiation operation is performed by an operator similar to the Laplacian operator. From the differentiated record’s, two parametric measures have been extracted and used as identifiers for the speaker; i.e. mean-value and number of zero-crossing points.