Abdul BasirMuhammad Adil KhanHidayat UllahYahya AlmalkiSaowaluck ChasreechaiThanin Sitthiwirattham2025-03-102025-03-102023Axioms2075168010.3390/axioms120908852-s2.0-85172096701https://repository.dusit.ac.th//handle/123456789/4560In the recent era of research developments, mathematical inequalities and their applications perform a very consequential role in different aspects, and they provide an engaging area for research activities. In this paper, we propose a new approach for the improvement of the classical majorization inequality and its weighted versions in a discrete sense. The proposed improvements give several estimates for the majorization differences. Some earlier improvements of the Jensen and Slater inequalities are deduced as direct consequences of the obtained results. We also discuss the conditions under which the main results give better estimates for the majorization differences. Applications of the acquired results are also presented in information theory. © 2023 by the authors.All Open Access; Gold Open Accessconvex functioninformation theoryJensenÕs inequalitymajorization inequalitySlaterÕs inequalityArticleScopus