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Hermite–Hadamard-Mercer Type Inequalities for Interval-Valued Coordinated Convex Functions
AxiomsDetermining the Jensen–Mercer inequality for interval-valued coordinated convex functions has been a challenging task for researchers in the fields of inequalities and interval analysis.
Muhammad Toseef +3 more
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UEG Week 2025 Moderated Posters [PDF]
United European Gastroenterol JUnited European Gastroenterology Journal, Volume 13, Issue S8, Page S189-S802, October 2025.
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The Jensen-Mercer Inequality with Infinite Convex Combinations
Mathematical Sciences and Applications E-Notes, 2019 The paper deals with discrete forms of double inequalities related to convex functions of one variable. Infinite convex combinations and sequences of convex combinations are included. The double inequality form of the Jensen-Mercer inequality and its variants are especially studied.
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AIMS Mathematics, 2021 <abstract><p>In this paper we find further versions of generalized Hadamard type fractional integral inequality for $ k $-fractional integrals. For this purpose we utilize the definition of $ h $-convex function. The presented results hold simultaneously for variant types of convexities and fractional integrals.</p></abstract>
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Inequalities for Products of Two Kinds of Convexities and Consequent Results
Journal of Mathematics, Volume 2026, Issue 1, 2026.The product of two convex functions is convex under certain conditions, which have motivated extensions to generalized convexities. In the present paper, we establish new Hermite–Hadamard–type inequalities for the product of m‐convex and (α, m)‐convex functions.
Abdur Rehman +4 more
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Journal of Mathematics, Volume 2026, Issue 1, 2026.We explore the features of fractional integral inequalities for some new classes of interval‐valued convex functions (CF s) to establish their generalization compared to the previously known real‐valued CF s. Motivated by the foundational role of mathematical inequalities in analysis and optimization, we delve into the formulation and proof of integral
Ahsan Fareed Shah +5 more
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Journal of Mathematics, Volume 2026, Issue 1, 2026.This paper investigates the class of interval‐valued s‐convex functions in the second sense sIVC2 using Caputo–Fabrizio CF integrals. Some generalizations of the Hermite–Hadamard HH‐type, Hermite–Hadamard–Fejér HHF‐type, and Hermite–Hadamard–Mercer HHM‐type inclusions involving the CF integrals are developed.
Ammara Nosheen +5 more
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New fractional estimates for Hermite-Hadamard-Mercer’s type inequalities
Alexandria Engineering Journal, 2020 An analogous version of Hermite-Hadamard-Mercer’s inequality has been established using the Katugampola fractional integral operators. The result is the generalization of the Riemann-Liouville fractional integral operator combined with the left and right
Hong-Hu Chu +3 more
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Newton–Simpson-type inequalities via majorization
Journal of Inequalities and Applications, 2023 In this article, the main objective is construction of fractional Newton–Simpson-type inequalities with the concept of majorization. We established a new identity on estimates of definite integrals utilizing majorization and this identity will lead us to
Saad Ihsan Butt +3 more
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Generalization of the Jensen-Mercer inequality by Taylor's polynomial [PDF]
Mathematical Inequalities & Applications, 2016 We present generalizations of the Jensen-Mercer inequality for the class of n-convex functions, obtained by using Taylor’s polynomial and Green function. By applying those inequalities we obtain some results related to Čebyšev functionals.
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