{"title":"A Sandwich-type Theorem with Applications to Univalent Functions","authors":"Sukhwinder Singh Billing, Sushma Gupta, Sukhjit Singh Dhaliwal","volume":33,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":751,"pagesEnd":757,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/2210","abstract":"In the present paper, we obtain a sandwich-type theorem.\r\nAs applications of our main result, we discuss the univalence\r\nand starlikeness of analytic functions in terms of certain differential\r\nsubordinations and differential inequalities.","references":"[1] S. S. Miller and P. T. Mocanu, Differential subordination and Univalent\r\nfunctions, Michigan Math. J. 28(1981), 157-171.\r\n[2] S. S. Miller and P. T. Mocanu, Differential Suordinations : Theory and\r\nApplications, Series on monographs and textbooks in pure and applied\r\nmathematics (No.225), Marcel Dekker, New York and Basel, 2000.\r\n[3] S. S. Miller and P. T. Mocanu, Subordinants of differential superordinations,\r\nComplex Variables, 48(10)(2003), 815-826.\r\n[4] K. Noshiro, On the theory of schlicht functions, J. Fac. Sci., Hokkaido\r\nUniv., 2(1934-35), 129-155.\r\n[5] M. Obradovic, S. Ponnusamy, V. Singh and P. Vasundhra, Differential\r\nInequalities and Criteria for Starlike and Univalent Functions, Rocky\r\nMountain J. Math., 36(1)(2006), 303-317.\r\n[6] Ch. Pommerenke, Univalent Functions, Vanderhoeck and Ruprecht,\r\nG\u252c\u00bfotingen, 1975.\r\n[7] S. E. Warchawski, On the higher derivatives at the boundary in conformal\r\nmappings, Trans. Amer. Math. Soc., 38(1935), 310-340.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 33, 2009"}