NEIGHBOURHOODS AND PARTIAL SUMS OF STARLIKE FUNCTIONS BASED ON RUSCHEWEYH DERIVATIVES

Abstract

ABSTRACT. In this paper a new class S λ p (α, β) of starlike functions is introduced. A subclass T S λ p (α, β) of S λ p (α, β) with negative coefficients is also considered. These classes are based on Ruscheweyh derivatives. Certain neighbourhood results are obtained. Partial sums fn(z) of functions f(z) in these classes are considered and sharp lower bounds for the ratios of real part of f(z) to fn(z) and f ′ (z) to f ′ n(z) are determined.