On New General Beesack-Opial-type Integral Inequalities
Abstract
This article presents new Beesack-Opial-type integral inequalities incorporating three functions. The upper bounds are defined using some derivatives and primitives of these functions. Detailed proofs are provided. These are accompanied by illustrative examples, including applications involving the Laplace transform.
References
Agarwal, R. P., & Pang, P. Y. H. (1995). Opial inequalities with applications in differential and difference equations. Mathematics and Its Applications (Vol. 320). Kluwer Academic Publishers. https://doi.org/10.1007/978-94-015-8426-5
Beesack, P. R. (1962). On an integral inequality of Z. Opial. Transactions of the American Mathematical Society, 104, 470–475. https://doi.org/10.1090/S0002-9947-1962-0139706-1
Cheung, W. S. (1990). Some new Opial-type inequalities. Mathematika, 37, 136–142. https://doi.org/10.1112/S0025579300012869
Cheung, W. S. (1991). Some generalized Opial-type inequalities. Journal of Mathematical Analysis and Applications, 162, 317–321. https://doi.org/10.1016/0022-247X(91)90152-P
Godunova, E. K., & Levin, V. I. (1967). On an inequality of Maroni (in Russian). Matematicheskie Zametki, 2, 221–224.
He, X. G. (1994). A short note on a generalization of Opial's inequality. Journal of Mathematical Analysis and Applications, 182, 299–300. https://doi.org/10.1006/jmaa.1994.1086
Maroni, P. (1967). Sur l'inégalité d'Opial-Beesack. Comptes Rendus de l'Académie des Sciences de Paris, Série A-B, 264, A62–A64.
Hua, L. K. (1965). On an inequality of Opial. Scientia Sinica, 14, 789–790.
Olech, C. (1960). A simple proof of a certain result of Z. Opial. Annales Polonici Mathematici, 8, 61–63. https://doi.org/10.4064/ap-8-1-61-63
Opial, Z. (1960). Sur une inégalité. Annales Polonici Mathematici, 8, 29–32. https://doi.org/10.4064/ap-8-1-29-32
Pachpatte, B. G. (1986). On Opial-type integral inequalities. Journal of Mathematical Analysis and Applications, 120, 547–556. https://doi.org/10.1016/0022-247X(86)90176-9
Pachpatte, B. G. (1993). Some inequalities similar to Opial's inequality. Demonstratio Mathematica, 26, 643–647. https://doi.org/10.1515/dema-1993-3-412
Pachpatte, B. G. (1999). A note on some new Opial type integral inequalities. Octogon Mathematical Magazine, 7, 80–84.
Pachpatte, B. G. (1994). On some inequalities of the Weyl type. Analele Ştiinţifice ale Universităţii “A. I. Cuza” din Iaşi. Serie Nouă. Matematică, 40, 89–95.
Saker, S. H., Abdou, M. D., & Kubiaczyk, I. (2018). Opial and Pólya type inequalities via convexity. Fasciculi Mathematici, 60, 145–159. https://doi.org/10.1515/fascmath-2018-0009
Salem, S. H., Agwo, H. A., & Khallaf, N. S. (2011). On the Opial-Beesack-Troy inequalities. International Journal of Mathematical Analysis, 5, 583–592.
Srivastava, H. M., Tseng, K.-L., Tseng, S.-J., & Lo, J.-C. (2010). Some weighted Opial-type inequalities on time scales. Taiwanese Journal of Mathematics, 14, 107–122. https://doi.org/10.11650/twjm/1500405730
Tatjana, M., & Tatjana, B. (2024). Opial inequalities for a conformable Δ-fractional calculus on time scales. Mathematica Moravica, 28, 17–32. https://doi.org/10.5937/MatMor2402017M
Zhao, C.-J., & Cheung, W.-S. (2014). On Opial-type integral inequalities and applications. Mathematical Inequalities and Applications, 17, 223–232. https://doi.org/10.7153/mia-17-17
Wong, F. H., Lian, W. C., Yu, S. L., & Yeh, C. C. (2008). Some generalizations of Opial's inequalities on time scales. Taiwanese Journal of Mathematics, 12, 463–471. https://doi.org/10.11650/twjm/1500574167
This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg){kind=logo}
