Inequalities of extended Beta and extended hypergeometric functions

Abstract

This paper studies the log-convexity of the extended beta functions. As a consequence, Tur\'an-type inequalities are established.The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the inequalities on extended beta functions,. The particular cases of those results also gives the Tur\'an-type inequalities for extended confluent and extended Gaussian hypergeometric functions. Some reverse of Tur\'an-type inequalities also derived.