Harmonic conformable refinements of Hermite-Hadamard Mercer inequalities by support line and related applications
| Autor: | Saad Ihsan Butt, Miguel Vivas-Cortez, Hira Inam |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Mathematical and Computer Modelling of Dynamical Systems, Vol 30, Iss 1, Pp 385-416 (2024) |
| Druh dokumentu: | article |
| ISSN: | 13873954 1744-5051 1387-3954 |
| DOI: | 10.1080/13873954.2024.2348156 |
| Popis: | ABSTRACTWe establish new conformable fractional Hermite-Hadamard (H–H) Mercer type inequalities for harmonically convex functions using the concept of support line. We introduce two new conformable fractional auxiliary equalities in the Mercer sense and apply them to differentiable functions with harmonic convexity. We also use Power-mean, Hölder’s and improved Hölder inequality to derive new Mercer type inequalities via conformable fractional integrals. The accuracy and superiority of the offered technique are clearly depicted through impactful visual illustrations. We also use our technique to derive new estimates for hypergeometric functions and special means of real numbers that are more precise than existing ones. Some applications are provided as well. Our results generalize and extend some existing ones in the literature. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|