Extending and Improving Monotonic Integral Inequalities
DOI:
https://doi.org/10.63286/jima.004Keywords:
integral inequalities, primitive, monotonicity, integral decompositions, second mean value theorem for definite integralsAbstract
Monotonic integral inequalities dealing with the product of two functions are standard in mathematics. In this article, we contribute to the subject by considering new assumptions. They innovate by taking into account the possible interaction of the involved functions, characterized by inequalities that mix primitive-like operators, derivatives and a certain parameter. This parameter plays a crucial role in the obtained bounds and their refinements.
References
[1] D. Bainov and P. Simeonov, Integral Inequalities and Applications, Mathematics and Its Applications, vol. 57, Kluwer Academic, Dordrecht, 1992.
[2] E. F. Beckenbach and R. Bellman, Inequalities, Springer, Berlin, 1961.
[3] Z. Cvetkovski, Inequalities: Theorems, Techniques and Selected Problems, Springer, Berlin, 2012.
[4] G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, Cambridge, 1934.
[5] W. Walter, Differential and Integral Inequalities, Springer, Berlin, 1970.
[6] B. C. Yang, Hilbert-Type Integral Inequalities, Bentham Science Publishers, The United Arab Emirates, 2009.
[7] W. S. Du, New integral inequalities and generalizations of Huang-Du's integral inequality, Applied Mathematical Sciences, 17(6), 2023, 265–272.
[8] C. Chesneau, Some lower bounds for a double integral depending on six adaptable functions, Proof, 4, 2024, 106–113.
DOI: 10.37394/232020.2024.4.10
[9] H. Huang and W. S. Du, On a new integral inequality: Generalizations and applications, Axioms, 11, 2022, 1–9.
[10] N. S. Hoang, Notes on an inequality, Journal of Inequalities in Pure and Applied Mathematics, 9(2), 2008, 1–5.
[11] W. J. Liu, C. C. Li, and J. W. Dong, On an problem concerning an integral inequality, Journal of Inequalities in Pure and Applied Mathematics, 8(3), 2007, 1–5.
[12] Q. A. Ngo, D. D. Thang, T. T. Dat, and D. A. Tuan, Notes on an integral inequality, Journal of Inequalities in Pure and Applied Mathematics, 7, 2006, 1–5.
[13] W. T. Sulaiman, Notes on integral inequalities, Demonstratio Mathematica, 41, 2008, 887–894.
[14] W. T. Sulaiman, New several integral inequalities, Tamkang Journal of Mathematics, 42, 2011, 505–510.
DOI: 10.5556/j.tkjm.42.2011.1035
[15] W. T. Sulaiman, Several ideas on some integral inequalities, Advances in Pure Mathematics, 1, 2011, 63–66.
[16] W. T. Sulaiman, A study on several new integral inequalities, South East Asian Journal of Mathematics, 42, 2012, 333–339.
[17] G. Zabadan, Notes on an open problem, Journal of Inequalities in Pure and Applied Mathematics, 9, 2008, 1–5.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Christophe Chesneau
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
