Let be the complex unit disc and be the class of all analytic functions in , normalized with the conditions . A function in is said to be in the class if in (, and ). For a nonnegative real-valued integrable function satisfying the normalizing condition and let
for some and and if, in addition is decreasing on (0,1), the authors prove their principal result, that states that , where is the subclass of consisting of starlike functions in . Some other results on the class and applications are also given.