Bullen–Simpson–Mercer type inequalities

The main objective of our paper is to establish a new set of Bullen–Simpson type inequalities concerning the Jensen–Mercer's inequality. At first, we derive a new general Bullen–Simpson–Mercer's identity, with which we get out primary consequences. Furthermore, considering the Bullen–Simpson–Mercer's identity, we use the convexity property together with Hölder type inequalities and Young’s inequalities, bounding, and Lipschitz characteristics of functions to get new variants of generalized upper bounds of Bullen–Simpson's inequality.