New variants of the Hermite–Hadamard–Mercer type estimates involving the Beta function with numerical analysis
Year: 2025
Type: article
Abstract: A refined form of the Jensen–Mercer inequality has recently been introduced in the literature. Utilizing this improved inequality, we derive several new variants of the Hermite–Hadamard–Mercer type inequality, along with related estimates involving the beta function. These results serve to extend and generalize various existing inequalities. To demonstrate the validity of our findings, we provide numerical examples supported by both graphical and computational analyses. In addition, we explore applications of our results to specific means, including the arithmetic, harmonic, geometric, logarithmic, and p -logarithmic means. We hope that this work will stimulate further investigations in this area.
Source: Boundary Value Problems
Author: Eze R. Nwaeze
Institution: Alabama State University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,890
OpenAlex ID: W4416942503