Generalization of Hermite-Hadamard-Mercer]{Generalization of
Hermite-Hadamard-Mercer and Trapezoid Formula Type Inequalities
Involving Beta Function
Abstract
In this work, we prove a generalized version of Hermite-Hadamard-Mercer
type inequalities using the Beta function. Moreover, we prove some new
trapezoidal type inequalities involving Beta functions for
differentiable convex functions. The main advantage of these
inequalities is that these can be converted into similar classical
integral inequalities, Riemann-Liouville fractional integral
inequalities and $k$-Riemann-Liouville fractional integral
inequalities. Finally, we give applications to special means of real
numbers for newly established inequalities.