On Partial Sums of Certain Analytic Functions

Abstract

Abstract. In the present paper we give some results concerning partial sums of certain analytic functions analogous to the results due to H. Silverman [J. Math. Anal. Appl. 209 (1997), 221-227]. All the results are sharp. IntroductionLet S denote the class of functions of the form:that are analytic (hence the series in (1.1) is convergent), and / is univalent in the open unit disc U = {z = \z\ < 1}. Let K(a) and S*(a) denote the subclasses of S that are, respectively, convex and starlike functions of order a, 0 < a < 1. For conveniece, we write K (

CERTAIN SUBCLASS OF ANALYTIC FUNCTION ASSOCIATED WITH A GENERALIZATION OF q−SALAGEAN OPERATOR WITH NEGATIVE COEFFICIENTS A. O. MOSTAFA, M. K. AOUF, R. E. EL- MORSY

“…(i) Letting q → 1 − and putting λ = 1 and γ = 0 in Theorems 12,13 and 14, we have results obtained by Mostafa [21];…”

“…We will follow the work of [32] and also the work cited in ( [10], [11], [15], [16], [24], [28] and [21]) on partial sums of analytic functions. Also, we will make use of the well-known results that ℜ…”