Some Inequalities of Extended Hypergeometric Functions

Abstract

Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent hypergeometric function, respectively, by virtue of Hölder integral inequality and Chebyshev’s integral inequality. We also studied the monotonicity, log-concavity, and log-convexity of extended hypergeometric functions, which are derived by using the inequalities on an extended beta function.

On inequalities of Simpson's type for convex functions via generalized fractional integrals

“…This subject has been studied by many scientists in terms of its widespread use [20,21,27,30,31,37,40,44]. One of the most important applications of the fractional Integrals is the Hermite-Hadamard integral inequality (see, [1,22,26,38,39,41]).…”