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Some generalizations of Mercer inequality and its operator extensions [PDF]
Miskolc Mathematical NotesWe give a more general form of the Mercer inequality by replacing some constants by positive operators. As some consequences, our results produce a Jensen operator inequality for superquadratic functions.
Mohsen Kian, Zainab Peymani
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Hermite–Jensen–Mercer Type Inequalities for Caputo Fractional Derivatives
Journal of Function Spaces, 2020 In this article, certain Hermite–Jensen–Mercer type inequalities are proved via Caputo fractional derivatives. We established some new inequalities involving Caputo fractional derivatives, such as Hermite–Jensen–Mercer type inequalities, for differentiable mapping hn whose derivatives in the absolute values are convex.
Jinchao Zhao +4 more
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Improvement and generalization of some Jensen-Mercer-type inequalities [PDF]
Journal of Mathematical Inequalities, 2020 The present paper is devoted to the study of Jensen-Mercer-type inequalities. Our results generalize and improve some earlier results in the literature.
Moradi, Hamid Reza, Furuichi, Shigeru
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Advances in Ostrowski-Mercer Like Inequalities within Fractal Space
Fractal and Fractional, 2023 The main idea of the current investigation is to explore some new aspects of Ostrowski’s type integral inequalities implementing the generalized Jensen–Mercer inequality established for generalized s-convexity in fractal space.
Miguel Vivas-Cortez +4 more
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JENSEN–MERCER INEQUALITY AND RELATED RESULTS IN THE FRACTAL SENSE WITH APPLICATIONS
Fractals, 2021 The most notable inequality pertaining convex functions is Jensen’s inequality which has tremendous applications in several fields. Mercer introduced an important variant of Jensen’s inequality called as Jensen–Mercer’s inequality. Fractal sets are useful tools for describing the accuracy of inequalities in convex functions.
Butt, Saad Ihsan +3 more
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Hermite–Hadamard–Mercer-Type Inequalities for Harmonically Convex Mappings
Mathematics, 2021 In this paper, we prove Hermite–Hadamard–Mercer inequalities, which is a new version of the Hermite–Hadamard inequalities for harmonically convex functions.
Xuexiao You +4 more
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Generalization of Jensen Mercer inequality on Delta integral with Applications
European Journal of Pure and Applied Mathematics, 2023 The aim of this article is to give generalization of Jensen Mercer inequality on deltaintegral along with applications to Ky Fan inequality and related results.
Sadia Chanan, Nazia Irshad, Afshan Khan
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New Majorized Fractional Simpson Estimates
Axioms, 2023 Fractional calculus has been a concept used to acquire new variants of some well-known integral inequalities. In this study, our primary goal is to develop majorized fractional Simpson’s type estimates by employing a differentiable function.
Xiaoye Ding +4 more
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Generalized Niezgoda's Inequality with Refinements and Applications [PDF]
Sahand Communications in Mathematical AnalysisMotivated by the results of Niezgoda, corresponding to the generalization of Mercer's inequality for positive weights, in this paper, we consider real weights, for which we establish related results.
Faiza Rubab +3 more
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New refinements of the Jensen-Mercer inequality associated to positive $n$-tuples
Armenian Journal of Mathematics, 2022 In this manuscript, we propose new refinements for the Jensen-Mercer as well as variant of the Jensen-Mercer inequalities associated to certain positive tuples. We give some related integral version and present applications for different means. At the end, further generalizations are given which are associated to $m$ finite sequences.
Muhammad Adil Khan, Josip Pečarić
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