The quasi-Hadamard products of certain subclasses of analytic p-valent functions with negative coefficients

Abstract

The object of the present paper is to investigate some quasi-Hadamard products of certain subclasses of analytic p-valent functions with negative coefficients in the open unit disc. Our results are the generalizations of the corresponding results due to Aouf and Darwish [M.K. Aouf, H.E. Darwish, Basic properties and characterizations of a certain class of analytic functions with negative coefficients. II, Utilitas Math. 46 (1994) 167–177], Aouf et al. [M.K. Aouf, H.M. Hossen, H.M. Srivastava, A certain subclass of analytic p-valent functions with negative coefficients, Demonstratio Math. 31 (1998) 595–608], Lee et al. [S.K. Lee, S. Owa, H.M. Srivastava, Basic properties and characterization of a certain class of analytic functions with negative coefficients, Utilitas Math. 36 (1989) 121–128] and Yaguchi et al. [T. Yaguchi, O. Kwon, N.E. Cho, R. Yamakawa, A generalization class of certain subclasses of p-valently analytic functions with negative coefficients, RIMS Kokyuroku (Kyoto) 821 (1993) 101–111].