Refinements of Majorization Inequality Involving Convex Functions via Taylor’s Theorem with Mean Value form of the Remainder

Wu, Shanhe; Khan, Muhammad Adil; Haleemzai, Hidayat Ullah

doi:10.3390/math7080663

Cited by 9 publications

(6 citation statements)

References 11 publications

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“…ey used the main result to obtain some extensions for the weighted Favard's inequality. Wu et al [23] obtained some refinements of majorizationtype inequalities with the help of Taylor theorem with the mean value form of the remainder and also presented an application. Ullah et al [24] established some improvements and generalizations of majorization-type inequalities with the help of a strongly convex function and also gave some applications of the obtained results.…”

Section: Theorem 4 Suppose That a Function ψmentioning

confidence: 99%

Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory

Deng

Ullah

Khan

et al. 2021

Journal of Mathematics

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In this study, we present some new refinements of the Jensen inequality with the help of majorization results. We use the concept of convexity along with the theory of majorization and obtain refinements of the Jensen inequality. Moreover, as consequences of the refined Jensen inequality, we derive some bounds for power means and quasiarithmetic means. Furthermore, as applications of the refined Jensen inequality, we give some bounds for divergences, Shannon entropy, and various distances associated with probability distributions.

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Section: Theorem 4 Suppose That a Function ψmentioning

confidence: 99%

Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory

Deng

Ullah

Khan

et al. 2021

Journal of Mathematics

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“…In 2019, Adil Khan et al [55] presented the extension of the classical majorization inequality and its weighted versions under different circumstances for convex functions on rectangles. Wu et al [56] acquired improvements of the majorization-type inequalities for convex functions through Taylor's theorem with a mean value form of remainder. In 2021, Deng et al [46] refined the Jensen inequality through the theory of majorization by a new method and further explained the importance of the refined inequality by providing its applications in various domains.…”

Section: Introductionmentioning

confidence: 99%

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

Basir,

Khan,

Ullah

et al. 2023

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In 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.

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“…In this extension, the authors considered certain monotonic tuples. Wu et al [38] gave some refinement of the majorization inequalities with the help of Taylor's theorem. They used a convex function whose double derivative exists on interval and various types of monotonic tuples.…”

Section: Introductionmentioning

confidence: 99%

“…. , m − 1 and tx j + (1 − t)y j + p j φ ty j + (1 − t)x j (38). Integration of(38) with respect to t, delivers φ…”

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Generalized Hermite-Hadamard-Mercer type inequalities via majorization

Faisal

Khan

Iqbal

2022

Filomat

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The Hermite-Hadamard inequality has been recognized as the most pivotal inequality which has grabbed the attention of several mathematicians. In recent years, load of results have been established for this inequality. The main theme of this article is to present generalized Hermite-Hadamard inequality via the Jensen-Mercer inequality and majorization concept. We establish a Hermite-Hadamard inequality of the Jensen-Mercer type for majorized tuples. With the aid of weighted generalized Mercer?s inequality, we also prove a weighted generalized Hermite-Hadamard inequality for certain tuples. The idea of obtaining the results of this paper, may explore a new way for derivation of several other results for Hermite-Hadamard inequality.

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Refinements of Majorization Inequality Involving Convex Functions via Taylor’s Theorem with Mean Value form of the Remainder

Cited by 9 publications

References 11 publications

Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory

Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory

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

Generalized Hermite-Hadamard-Mercer type inequalities via majorization

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