Some Properties of Convolution Operators in the Class Pα(β)

Making use of several families of convolution operators, we introduce and study a certain general class Pα(β) (0 ≦ α < 1; β ≧ 0) of analytic functions in the open unit disk U. We also investigate the relationships between the class Pα(β) and the Hardy space H∞ (of bounded analytic functions in U). Finally, we consider some interesting applications of the results presented here to a class of generalized hypergeometric functions.