New estimates on generalized Hermite-Hadamard-Mercer-type inequalities

The concept of a convex function plays a crucial role in fields of mathematical analysis and inequality theory. The importance of convex functions is exemplified by Mercer's inequality. This inequality, which is derived through the application of convex functions, has been extensively studied and is a subject of considerable interest within the mathematical community. This paper presents new generalizations related to Mercer's inequality and compares the inequalities obtained for different values of n with those presented in the existing literature. Also, this study presents pioneering contributions to the field, and we believe that the results in this study will enhance further research on the topic.