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Within the recent wave of research advancements, mathematical inequalities and their practical applications play a notably significant role across various domains. In this regard, inequalities offer a captivating arena for scholarly endeavors and investigational pursuits. This research work aims to present new improvements for the integral majorization inequalities using an interesting aproach. Certain previous improvements have been achieved for the Jensen inequality as direct outcomes of the main results. Additionally, estimates for the Csiszár divergence and its cases are provided as applications of the main results. The circumstances under which the principal outcomes offer enhanced estimations for majorization differences are also underscored and emphasized.