Difference equations related to majorization theorems via Montgomery identity and Green’s functions with application to the Shannon entropy

Siddique, Nouman; Imran, Muhammad; Khan, Khuram Ali; Pečarić, Josip

doi:10.1186/s13662-020-02884-7

Cited by 7 publications

(2 citation statements)

References 30 publications

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“…Some present-day applications of majorization theory in signal processing and communication can be traced to [20,21]. For more successive works carried out via the concept of majorization, one can see [22,23] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

New “Conticrete” Hermite–Hadamard–Jensen–Mercer Fractional Inequalities

Faisal

Khan

et al. 2022

Symmetry

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The theory of symmetry has a significant influence in many research areas of mathematics. The class of symmetric functions has wide connections with other classes of functions. Among these, one is the class of convex functions, which has deep relations with the concept of symmetry. In recent years, the Schur convexity, convex geometry, probability theory on convex sets, and Schur geometric and harmonic convexities of various symmetric functions have been extensively studied topics of research in inequalities. The present attempt provides novel portmanteauHermite–Hadamard–Jensen–Mercer-type inequalities for convex functions that unify continuous and discrete versions into single forms. They come as a result of using Riemann–Liouville fractional operators with the joint implementations of the notions of majorization theory and convex functions. The obtained inequalities are in compact forms, containing both weighted and unweighted results, where by fixing the parameters, new and old versions of the discrete and continuous inequalities are obtained. Moreover, some new identities are discovered, upon employing which, the bounds for the absolute difference of the two left-most and right-most sides of the main results are established.

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Section: Introductionmentioning

confidence: 99%

New “Conticrete” Hermite–Hadamard–Jensen–Mercer Fractional Inequalities

Faisal

Khan

et al. 2022

Symmetry

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“…Zaheer et al [40] obtained integral inequalities related to strongly convex functions using majoriaztion. For more recent results, we refer the reader to [36,37].…”

Section: Introductionmentioning

confidence: 99%

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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