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Generalization and refinements of the Jensen-Mercer inequality with applications [PDF]
Journal of Mathematical Inequalities, 2021 Summary: We give a generalization followed by refinements of Jensen-Mercer inequality in variety of ways. We also highlight its importance by stating plenty of applications. In this way our main results generalize many established results including Ky Fan's Inequality, Popoviciu's inequalities and Rado's inequalities etc.
Khan, Asif R. +2 more
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New “Conticrete” Hermite–Hadamard–Jensen–Mercer Fractional Inequalities [PDF]
Symmetry, 2022 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.
Shah Faisal +5 more
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Alexandria Engineering Journal, 2023 The objective of the current article is to incorporate the concepts of convexity and Jensen-Mercer inequality with the Caputo-Fabrizio fractional integral operator.
Soubhagya Kumar Sahoo +4 more
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On the refinements of Jensen Mercer's inequality
Journal of Numerical Analysis and Approximation Theory, 2012 In this paper we give refinements of Jensen-Mercer's inequality and its generalizations and give applications for means. We prove \(n\)-exponential convexity of the functions constructed from these refinements. At the end we discuss some examples.
Muhammad Adil Khan +2 more
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On a variant of the Jensen-Mercer inequality for operators [PDF]
Journal of Mathematical Inequalities, 2008 Some refinements of the Jensen-Mercer inequality for operators are presented. Obtained results are used to refine some comparision inequalities between power and quasi-arithmetic means for operators.
Matković, Anita, Pečarić, Josip
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On Some New Ostrowski–Mercer-Type Inequalities for Differentiable Functions
Axioms, 2022 In this paper, we establish a new integral identity involving differentiable functions, and then we use the newly established identity to prove some Ostrowski–Mercer-type inequalities for differentiable convex functions.
Ifra Bashir Sial +4 more
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New Estimates for Csiszár Divergence and Zipf–Mandelbrot Entropy via Jensen–Mercer’s Inequality
Complexity, 2020 Jensen’s inequality is one of the fundamental inequalities which has several applications in almost every field of science. In 2003, Mercer gave a variant of Jensen’s inequality which is known as Jensen–Mercer’s inequality. The purpose of this article is
Muhammad Adil Khan +2 more
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Journal of Mathematics, 2020 In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators ...
Qiong Kang +5 more
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Journal of Inequalities and Applications, 2023 In this investigation, we unfold the Jensen–Mercer ( J − M $\mathtt{J-M}$ ) inequality for convex stochastic processes via a new fractional integral operator.
Fahd Jarad +5 more
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Reverse Jensen-Mercer Type Operator Inequalities
The Electronic Journal of Linear Algebra, 2016 Let $A$ be a selfadjoint operator on a Hilbert space $\mathcal{H}$ with spectrum in an interval $[a,b]$ and $\phi:B(\mathcal{H})\rightarrow B(\mathcal{K})$ be a unital positive linear map, where $\mathcal{K}$ is also a Hilbert space.
Anjidani, Ehsan +1 more
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