Inequalities of extended beta and extended hypergeometric functions

J Inequal Appl. 2017;2017(1):10. doi: 10.1186/s13660-016-1276-9. Epub 2017 Jan 6.

Abstract

We study the log-convexity of the extended beta functions. As a consequence, we establish Turán-type inequalities. 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 give the Turán-type inequalities for extended confluent and extended Gaussian hypergeometric functions. Some reverses of Turán-type inequalities are also derived.

Keywords: Turán-type inequalities; extended beta functions; extended hypergeometric functions; log-convexity.