SOME GENERALIZED RESULTS BASED ON DIFFERENTIAL SUBORDINATIONS OF ANALYTIC FUNCTIONS

Document Type : Research Paper

Authors

DEPARTMENT OF MATHEMATICS, PAYAME NOOR UNIVERSITY, TEHRAN, IRAN

10.22103/jmmrc.2021.16816.1126

Abstract

For the function f(z) analytic in the open unit disk and normalized by f(0) = f0(0)−1 = 0, we consider the expression; ( zf0(z)f(z)−1)+1−( zf(z) );( > 0). Using differential subordination notion, we investigate properties of ( f(z) z ) , as well as, sufficient conditions for univalence and starlikeness of f(z). In the special case, for = 1, these results generalize and improve some previously results given in the literature.

Keywords


P. L. Duren, Univalent Function, Springer-verlag, 1983.
S. S. Miller and P. T. Mocanu, Di erential Subordination, Theory and Applications, Marcel Dekker, New York, Basel, 2000.
S. Ponnusamy and P. Vasundhra, Criteria for univalence, starlikeness and convexity, Ann. Polon. Math., 85, (2005), 121-133.
F. Ronning, S. Ruscheweyh and S. Samaris, Sharp starlikeness conditions for analytic functions with bounded derivative, J. Aust. Math. Soc. (Series A)69(2000), 303-315.
N. Tuneski and M. Obradovic, Some Properties of certain expressions of analytic functions, Comput. Math. Appl., 62, (2011), 3438-3445.