On order of convexity of functions defined by certain integral transforms

Abstract

For real-valued, monotonically decreasing on [0, 1] satisfying the conditions as t→0+ and increasing on (0, 1), we obtain that for a suitable f (z), where Using this result we obtain several other general results. We determine the least value of β so that for g analytic in and for the functions and are convex of order γ. Here 2F 1 is the Gaussian hypergeometric function. We have extended these results to functions of the form Corresponding starlikeness result is obtained for such convex combinations.