{"title":"Differential Sandwich Theorems with Generalised Derivative Operator","authors":"Maslina Darus, Khalifa Al-Shaqsi","volume":14,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":149,"pagesEnd":153,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/13046","abstract":"In this paper, a generalized derivatives operator n\r\n\u03bb,\u03b2f\r\nintroduced by the authors will be discussed. Some subordination and\r\nsuperordination results involving this operator for certain normalized\r\nanalytic functions in the open unit disk will be investigated. Our\r\nresults extend corresponding previously known results.","references":"[1] F. M. Al-Oboudi, On univalent functions defined by a generalized\r\nS\u2566\u00ffal\u2566\u00ffagean operator, Ind. J. Math. Math. Sci. 27, (2004), 1429-1436.\r\n[2] G. S\u252c\u00a9 . S\u2566\u00ffal\u2566\u00ffagean, Subclasses of univalent functions, Lecture Note in\r\nMath.(Springer-Verlag), 1013, (1983), 362-372.\r\n[3] K. Al-Shaqsi and M. Darus, Differential subordination with generalized\r\nderivative operator. (Submitted)\r\n[4] K. Al Shaqsi and M. Darus, On univalent functions with respect to\r\nk-symmetric points defined by a generalized Ruscheweyh derivatives\r\noperator.(Submitted)\r\n[5] S. S. Miller and P. T. Mocanu, Subordinants of differential superordinations,\r\nComplex Variables Theory Appl. 48(10), (2003), 815-826.\r\n[6] St. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math.\r\nSoc. 49, (1975), 109-115.\r\n[7] S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and\r\nApplications, Marcel Dekker Inc., New York, 2000.\r\n[8] T. Bulboac\u2566\u00ffa, Classes of first order differential superordinations, Demonstratio\r\nMath. 35(2), (2002), 287-292.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 14, 2008"}