Inclusion relations and convolution properties of a certain class of analytic functions associated with the Ruscheweyh derivatives

Abstract

Let A denote the class of functions f ( z ) with f ( 0 ) = f ′ ( 0 ) − 1 = 0 , which are analytic in the open unit disk U . By means of the Ruscheweyh derivatives, we introduce and investigate the various properties and characteristics of a certain two-parameter subclass T ( α , λ ; h ) of A , where α ≧ 0 , λ > − 1 , and h ( z ) is analytic and convex univalent in U with h ( 0 ) = 1 . In particular, some inclusion relations and convolution properties for the function class T ( α , λ ; h ) are presented here.