In the present investigation, by making use of strong differential subordinations and superordinations, we introduce and study two new classes of holomorphic functions containing generalized differential operator. Also we determine important properties for functions belongs to these classes.
If the inline PDF is not rendering correctly, you can download the PDF file here.
 A. A. Lupaş, A note on special strong differential superordinations using multiplier transformation, Journal of Computational Analysis and Applications, vol. 17, no. 4, 2014, 746-751.
 F. M. Al-Oboudi, On univalent functions defined by a generalized Sălăgean operator, Int. J. Math. Math. Sci., vol. 27, 2004, 1429-1436.
 A. Amourah, M. Darus, Some properties of a new class of univalent functions involving a new generalized differential operator with negative coefficients, Indian J. Sci. Tech., vol. 9, no. 36, 2016, 1-7.
 N. E. Cho, T. H. Kim, Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc., vol. 40, no. 3, 2003, 399-410.
 N. E. Cho, O. S. Kwon, H. M. Srivastava, Strong differential subordination and superordination for multivalently meromorphic functions involving the Liu- Srivastava operator, Integral transforms Spec. Funct., vol. 21, no. 8, 2010, 589-601.
 M. Darus, R. W. Ibrahim, On subclasses for generalized operators of complex order, Far East J. Math. Sci., vol. 33, no. 3, 2009, 299-308.
 M. P. Jeyaraman, T. K. Suresh, Strong differential subordination and superordination of analytic functions, J. Math. Anal. Appl., vol. 385, no. 2, 2012, 854-864.
 S. S. Miller, P. T. Mocanu, Differential Subordinations. Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, vol. 225, Marcel Dekker Inc., New York, Basel, 2000.
 G. I. Oros, Strong differential superordination, Acta Universitatis Apulensis, vol. 19, 2009, 101-106.
 G. St. Sălăgean, Subclasses of univalent functions, Lecture Notes in Math., Springer Verlag, Berlin, vol. 1013, 1983, 362-372.
 A. K. Wanas, A. A. Lupaş, On a new strong differential Subordinations and superordinations of analytic functions involving the generalized differential operator, Int. J. Pure Appl. Math., vol. 116, no. 3, 2017, 571-579.
 A. K. Wanas, A. H. Majeed, New strong differential subordinations and superordinations of symmetric analytic functions, Int. J. Math. Anal., vol. 11, no. 11, 2017, 543-549.