Results 51 to 60 of about 185 (156)

Improvement in Some Inequalities via Jensen–Mercer Inequality and Fractional Extended Riemann–Liouville Integrals

Axioms, 2023
The primary intent of this study is to establish some important inequalities of the Hermite–Hadamard, trapezoid, and midpoint types under fractional extended Riemann–Liouville integrals (FERLIs).
Abd-Allah Hyder, Areej A. Almoneef, Hüseyin Budak   +2 more
doaj   +1 more source

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.
openaire   +5 more sources

Fractional version of the Jensen-Mercer and Hermite-Jensen-Mercer type inequalities for strongly h-convex function

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>
openaire   +3 more sources

Fractional Integral Inequalities for Generalized Interval‐Valued Functions With Applications in Stock Price Prediction via LSTM

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, Patricia J. Y. Wong, Nasir Rehman, Salah Mahmoud Boulaaras, Muhammad Shoaib Saleem, B. B Upadhyay   +5 more
wiley   +1 more source

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, Saima Rashid, Zakia Hammouch, Yu-Ming Chu   +3 more
doaj   +1 more source

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, Iram Javed, Praveen Agarwal, Juan J. Nieto   +3 more
doaj   +1 more source

Some Novel Inclusions for Interval‐Valued s‐Convex Functions in the Second Sense Involving Caputo–Fabrizio Integrals

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, Khuram Ali Khan, Mariam Aslam, Atiq ur Rehman, Demco K. Mukongo, Smritijit Sen   +5 more
wiley   +1 more source

New Hermite–Jensen–Mercer-type inequalities via k-fractional integrals

Advances in Difference Equations, 2020
In the article, we establish serval novel Hermite–Jensen–Mercer-type inequalities for convex functions in the framework of the k-fractional conformable integrals by use of our new approaches.
Saad Ihsan Butt, Muhammad Umar, Saima Rashid, Ahmet Ocak Akdemir, Yu-Ming Chu   +4 more
doaj   +1 more source

Green’s Function Approach to Hermite–Hadamard–Mercer Type Fractional Inequalities and Applications

Journal of Mathematics, Volume 2026, Issue 1, 2026.
The Hermite–Hadamard–Mercer (HHM) inequality, existing in two well‐established forms, plays a fundamental role in mathematical analysis. This inequality is characterized by three distinct components—namely, the left, middle, and right terms. This study is concerned to obtain novel generalized and refined HHM fractional inequalities by employing for the
Muhammad Zafran, Muhammad Adil Khan, Tahir Ullah Khan, Božidar Ivanković, Z. M. M. M. Sayed, Mohamed Sharaf, Francisco J. Garcia-Pacheco   +6 more
wiley   +1 more source

Refined Error Estimates for Milne–Mercer-Type Inequalities for Three-Times-Differentiable Functions with Error Analysis and Their Applications

Fractal and Fractional
In this study, we examine the error bounds related to Milne-type inequalities and a widely recognized Newton–Cotes method, originally developed for three-times-differentiable convex functions within the context of Jensen–Mercer inequalities. Expanding on
Arslan Munir, Shumin Li, Hüseyin Budak, Artion Kashuri, Loredana Ciurdariu   +4 more
doaj   +1 more source