Results 11 to 20 of about 250 (112)

The Hermite–Hadamard–Mercer Type Inequalities via Generalized Proportional Fractional Integral Concerning Another Function

International Journal of Mathematics and Mathematical Sciences, 2022
In order to be able to study cosmic phenomena more accurately and broadly, it was necessary to expand the concept of calculus. In this study, we aim to introduce a new fractional Hermite–Hadamard–Mercer’s inequality and its fractional integral type ...
Tariq A. Aljaaidi, Deepak B. Pachpatte
doaj   +3 more sources

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, Muhammad Aamir Ali, Hüseyin Budak, Jiraporn Reunsumrit, Thanin Sitthiwirattham   +4 more
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k -Fractional Variants of Hermite-Mercer-Type Inequalities via s-Convexity with Applications

Journal of Function Spaces, 2021
This article is aimed at studying novel generalizations of Hermite-Mercer-type inequalities within the Riemann-Liouville k-fractional integral operators by employing s-convex functions. Two new auxiliary results are derived to govern the novel fractional
Saad Ihsan Butt, Jamshed Nasir, Shahid Qaisar, Khadijah M. Abualnaja   +3 more
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fixed point, ψ-contraction, r-hybrid ψ-contraction, dynamic programming, integral equation

AIMS Mathematics, 2021
In this work, we establish inequalities of Hermite-Hadamard-Mercer (HHM) type for convex functions by using generalized fractional integrals. The results of our paper are the extensions and refinements of Hermite-Hadamard (HH) and Hermite-Hadamard-Mercer
Miguel Vivas-Cortez, Muhammad Aamir Ali, Artion Kashuri, Hüseyin Budak   +3 more
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New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function

Journal of Function Spaces, 2021
In 2003, Mercer presented an interesting variation of Jensen’s inequality called Jensen–Mercer inequality for convex function. In the present paper, by employing harmonically convex function, we introduce analogous versions of Hermite–Hadamard ...
Saad Ihsan Butt, Saba Yousaf, Atifa Asghar, Khuram Ali Khan, Hamid Reza Moradi   +4 more
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New midpoint type Hermite-Hadamard-Mercer inequalities pertaining to Caputo-Fabrizio fractional operators

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, Y.S. Hamed, Pshtiwan Othman Mohammed, Bibhakar Kodamasingh, Kamsing Nonlaopon   +4 more
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Some New Improvements for Fractional Hermite–Hadamard Inequalities by Jensen–Mercer Inequalities

Journal of Function Spaces
This article’s objective is to introduce a new double inequality based on the Jensen–Mercer JM inequality, known as the Hermite–Hadamard–Mercer inequality. We use the JM inequality to build a number of generalized trapezoid-type inequalities.
Maryam Gharamah Ali Alshehri, Abd-Allah Hyder, Hüseyin Budak, Mohamed A. Barakat   +3 more
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Some new generalized κ–fractional Hermite–Hadamard–Mercer type integral inequalities and their applications

AIMS Mathematics, 2022
In this paper, we have established some new Hermite–Hadamard–Mercer type of inequalities by using κ–Riemann–Liouville fractional integrals. Moreover, we have derived two new integral identities as auxiliary results.
Miguel Vivas-Cortez, Muhammad Uzair Awan, Muhammad Zakria Javed, Artion Kashuri, Muhammad Aslam Noor, Khalida Inayat Noor   +5 more
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New stochastic fractional integral and related inequalities of Jensen–Mercer and Hermite–Hadamard–Mercer type for convex stochastic processes

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, Soubhagya Kumar Sahoo, Kottakkaran Sooppy Nisar, Savin Treanţă, Homan Emadifar, Thongchai Botmart   +5 more
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New estimates on generalized Hermite–Hadamard–Mercer-type inequalities

Boundary Value Problems
The concept of a convex function plays a crucial role in fields of mathematical analysis and inequality theory. The importance of convex functions is exemplified by Mercer’s inequality.
Çetin Yıldız, Samet Erden, Seth Kermausuor, Daniel Breaz, Luminiţa-Ioana Cotîrlă   +4 more
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