Certain sufficient conditions for parabolic starlike and uniformly close-to-convex functions
Keywords:
Analytic function, univalent function, parabolic starlike function, uniformly close-to-convex function, differential subordination.Abstract
In the present paper, we study certain differential subordinations and obtain sufficient conditions for parabolic starlikeness and uniformly close-toconvexity of analytic functions.
Mathematics Subject Classification (2010): 30C80, 30C45.
References
Al-Amiri, H.S., Reade, M.O., On a linear combination of some expressions in the theory of univalent functions, Monatshefto fur Mathematik, 80(1975), 257-264.
Billing, S.S., Gupta, S., Dhaliwal, S.S., Certain differential inequalities involving multivalent functions, Int. J. Open Problems Complex Analysis, 3(2011), no. 2, 43-49.
Lewandowski, Z., Miller, S.S., Zlotkiewicz, E., Generating functions for some classes of univalent functions, Proc. Amer. Math. Soc., 56(1976), 111-117.
Ma, W.C., Minda, D., Uniformly convex functions, Ann. Polon. Math., 57(1992), no. 2, 165-175.
Miller, S.S., Mocanu, P.T., Reade, M.O., All α convex functions are univalent and starlike, Proc. Amer. Math. Soc., 37(1973), 553-554.
Miller, S.S., Mocanu, P.T., Differential subordination: Theory and applications, Marcel Dekker, New York and Basel, 2000.
Obradovic, M., Tuneski, N., On the starlike criteria defined by Silverman, Zeszyty Nauk. Politech. Rzeszowskiej. Mat., 181(2000), no. 24, 59-64.
Ronning, F., Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118(1993), no. 1, 189-196.
Silverman, H., Convex and starlike criteria, Int. J. Math. and Math. Sci., 22(1999), no. 1, 75-79.
Singh, S., Gupta, S., Singh, S., On a problem of univalence of functions satisfying a differential inequality, Math. Inequal. Appl., 10(2007), no. 1, 95-98.
Singh, V., Singh, S., Gupta, S., A problem in the theory of univalent functions, Integral Transforms and Special Functions, 16(2005), no. 2, 179-186.
Tuneski, N., On the quotient of the representations of convexity and starlikeness, Math. Nachr., 248-249(2003), no. 1, 200-203.
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