Generalization of Hermite–hadamard–mercer and Trapezoid Formula Type Inequalities Involving the Beta Function

We prove a generalized version of Hermite–Hadamard–Mercer type inequalities using the beta function. Moreover, we prove some new trapezoidal type inequalities involving the beta function 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.