New Montgomery-Mercer identity and associated integral inequalities with applications

Abstract

In this study, we focus on the Jensen-Mercer inequality and the Montgomery-Mercer identity to develop new error bounds for Ostrowski quadrature schemes. To wrap up this task, initially, we introduce a new equality connected to Montgomery's identity invoking the Mercer concept. We then apply the Montgomery-Mercer identity to establish some updated bounds for rectangular and mid-point schemes involving convex mappings and famously known inequalities like H\"{o}lder's and power-mean. Also, we explore some special cases that stem from our main findings, conduct numerical tests, and visual analysis, and present applications related to means.