New Results on a Fractional Integral of Extended Dziok-Srivastava Operator Regarding Strong Subordinations and Superordinations

In 2012, new classes of analytic functions on U x U- with coefficient holomorphic functions in U were defined to give a new approach to the concepts of strong differential subordination and strong differential superordination. Using those new classes, the extended Dziok-Srivastava operator is introduced in this paper and, applying fractional integral to the extended Dziok-Srivastava operator, we obtain a new operator D-z(-gamma) H-l (m) [alpha(1), beta(1)] that was not previously studied using the new approach on strong differential subordinations and superordinations. In the present article, the fractional integral applied to the extended Dziok-Srivastava operator is investigated by applying means of strong differential subordination and superordination theory using the same new classes of analytic functions on U U-. Several strong differential subordinations and superordinations concerning the operator D-z(-gamma) H-l (m) [alpha(1), beta(1)] are established, and the best dominant and best subordinant are given for each strong differential subordination and strong differential superordination, respectively. This operator may have symmetric or asymmetric properties.