Derivation of Bounds for Majorization Differences by a Novel Method and Its Applications in Information Theory

Basir, Abdul; Khan, Muhammad Adil; Ullah, Hidayat; Almalki, Yahya; Chasreechai, Saowaluck; Sitthiwirattham, Thanin

doi:10.3390/axioms12090885

Cited by 3 publications

(1 citation statement)

References 55 publications

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“…Remark 6. In the article [50], Basir et al discovered the discrete versions of the above aforementioned results.…”

Section: Corollarymentioning

confidence: 94%

Improvements of Integral Majorization Inequality with Applications to Divergences

Basir,

Khan,

Ullah

et al. 2023

Axioms

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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.

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“…Remark 6. In the article [50], Basir et al discovered the discrete versions of the above aforementioned results.…”

Section: Corollarymentioning

confidence: 94%

Improvements of Integral Majorization Inequality with Applications to Divergences

Basir,

Khan,

Ullah

et al. 2023

Axioms

Self Cite

View full text Add to dashboard Cite

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Improvements of the integral Jensen inequality through the treatment of the concept of convexity of thrice differential functions

Sohail,

Khan,

Ding

et al. 2024

MATH

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<p>Jensen's inequality, with its broad applications across various fields, presents an important subject for investigation and research. In this article, we introduce novel enhancements to Jensen's inequality by utilizing the convexity properties of a thrice differentiable function in the absolute sense. We conducted numerical experiments to compare our primary results with previously established findings. Additionally, we provided several applications of our major results to classical inequalities, means, and divergences.</p>

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Further improvements of the Jensen inequality in the integral sense by virtue of 6-convexity along with applications

Sohail,

Khan,

Nasr

et al. 2024

MATH

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<abstract><p>The Jensen inequality is of fundamental importance because of its influential and interesting consequences. In recent years, the Jensen inequality has been supposed to be the most engaging source for research. We present interesting improvements to the continuous version of Jensen's inequality through the application of the concept of 6-convexity. For real visualization and comparison to other results, some numerical experiments were provided. With the aid of the acquired results, improvements for the Hermite-Hadamard and Hölder inequalities were presented. Some relationships between the means were granted as applications of established improvements. In addition, some estimations of the Csiszár divergence and its associated cases were received as further applications of the obtained results. The major techniques employed in formulating the proposed improvements included the Jensen inequality and the concept of convexity.</p></abstract>

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Derivation of Bounds for Majorization Differences by a Novel Method and Its Applications in Information Theory

Cited by 3 publications

References 55 publications

Improvements of Integral Majorization Inequality with Applications to Divergences

Improvements of Integral Majorization Inequality with Applications to Divergences

Improvements of the integral Jensen inequality through the treatment of the concept of convexity of thrice differential functions

Further improvements of the Jensen inequality in the integral sense by virtue of 6-convexity along with applications

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