the present paper, using the technique of differential subordination, we obtain certain results for analytic functions defined by a multiplier transformation in the open unit disc E = { z : IzI < 1}. We claim that our results extend and generalize the existing results in this particular direction<\/p>\r\n","references":"[1] B. A. Uralegaddi and C. Somanatha, Certain classes of univalent func-tions, in Current Topics in Analytic Function Theory, H. M. Srivastava and S. Owa (ed.), World Scientific, Singapore, (1992), 371-374.\r\n[2] B. A. Uralegaddi, Certain subclasses of analytic functions, New Trends In Geometric Functions Theory and Applications. (Madras, 1990) 159-161, World Scientific Publishing Company, Singapore, New Jersey, Londan and Hong Kong, 1991.\r\n[3] Ch. Pommerenke, Univalent Functions, Vanderhoeck and Ruprecht, G6tingen, 1975.\r\n[4] G. M. Golusin, Some estimates for coefficients of univalent functions, (Russian), Math.Sb., 2(1938), No. 3(45), 321-330.\r\n[5] G. S. Salagean, Subclasses of univalent functions, Lecture Notes in Math., 1013, 362-372, Springer-Verlag, Heideberg, 1983.\r\n[6] Jian Li and S. Owa, Properties of the Said gean operator, Georgian Math. J., 5(4)(1998), 361-366.\r\n[7] N. E. Cho and H. M. Srivastava, Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling, 37(2003), 39-49.\r\n[8] N. E. Cho and T. H. Kim, Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc., 40(2003), 399-410.\r\n[9] R. Aghalary, R. M. Ali, S. B. Joshi and V. Ravichandran, Inequalities for analytic functions defined by certain linear operators, Int. J. Math. Sci., 4(2005), 267-274.\r\n[10] S. Owa, C. Y. Shen and M. Obradovi6, Certain subclasses of analytic functions, Tamkang J. Math., 20(1989), 105-115.\r\n[11] S. S. Miller and P. T. Mocanu, Second-order differential inequalities in the complex plane, J. Math. Anal. Appl., 65(1978), 289-305.\r\n[12] S. S. Miller and P. T. Mocanu, Differential subordination and Univalent functions, Michigan Math. J., 28(1981), 157-171.\r\n[13] Miller, S. S. and Mocanu, RT., Differential Suordinations : Theory and Applications, Series on monographs and textbooks in pure and applied mathematics (No. 225), Marcel Dekker, New York and Basel, 2000.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 31, 2009"}