Results 111 to 120 of about 7,920 (230)

Korovkin type theorems and approximate Hermite–Hadamard inequalities

Journal of Approximation Theory, 2012
Let \(X\) be a real linear space and let \(D \subset X\) be a convex subset. One can easily see that, for any constant \(\varepsilon \geq 0\), the \(\varepsilon\)-convexity of \(f\), i.e., the validity of \[ f(tx+(1-t)y)\leq t f(x) + (1-t) f(y) +\varepsilon \qquad (x,y\in D, \;t\in [0,1]), \] implies the following lower and upper \(\varepsilon ...
Makó, Judit, Páles, Zsolt
openaire   +2 more sources

Some Novel Inequalities for Godunova–Levin Preinvex Functions via Interval Set Inclusion (⊆) Relation

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this note, we introduce the concept of ℏ‐Godunova–Levin interval‐valued preinvex functions. As a result of these novel notions, we have developed several variants of Hermite–Hadamard and Fejér‐type inequalities under inclusion order relations. Furthermore, we demonstrate through suitable substitutions that this type of convexity unifies a variety of
Zareen A. Khan, Waqar Afzal, Mujahid Abbas, Kwara Nantomah, Ding-Xuan Zhou   +4 more
wiley   +1 more source

Conformable Fractional Integrals Versions of Hermite-Hadamard Inequalities and Their Generalizations

Journal of Function Spaces, 2018
We prove new Hermite-Hadamard inequalities for conformable fractional integrals by using convex function, s-convex, and coordinate convex functions. We prove new Montgomery identity and by using this identity we obtain generalized Hermite-Hadamard type ...
Muhammad Adil Khan, Yu-Ming Chu, Artion Kashuri, Rozana Liko, Gohar Ali   +4 more
doaj   +1 more source

Inequalities for B $\mathbb{B}$-convex functions via generalized fractional integral

Journal of Inequalities and Applications, 2019
Recently, fractional calculus has become a very popular and important area. Specially, fractional integral inequalities have been studied by different authors.
Ilknur Yesilce
doaj   +1 more source

Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels

Fractal and Fractional
This paper introduces new versions of Hermite–Hadamard, midpoint- and trapezoid-type inequalities involving fractional integral operators with exponential kernels.
Hong Li, B. Meftah, Wedad Saleh, Hongyan Xu, A. Kiliçman, Abdelghani Lakhdari   +5 more
semanticscholar   +1 more source

Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

Journal of Inequalities and Applications, 2020
In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined
Dafang Zhao, M. Ali, A. Kashuri, H. Budak, M. Sarıkaya   +4 more
semanticscholar   +1 more source

Sharp Integral Inequalities of the Hermite–Hadamard Type

Journal of Approximation Theory, 2002
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Guessab, Allal, Schmeisser, Gerhard
openaire   +2 more sources

On Improved Simpson‐Type Inequalities via Convexity and Generalized Fractional Operators

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this work, we develop novel Simpson‐type inequalities for mappings with convex properties by employing operators for tempered fractional integrals. These findings expand upon and refine classical results, including those linked to Riemann–Liouville fractional integrals.
Areej A. Almoneef, Abd-Allah Hyder, Fatih Hezenci, Hüseyin Budak, Pramita Mishra   +4 more
wiley   +1 more source

Hermite–Hadamard- and Pachpatte-type integral inequalities for generalized subadditive functions in the fractal sense

Miskolc Mathematical Notes
In this paper, we establish the generalized Hermite–Hadamard- and Pachpatte-type integral inequalities for local fractional integrals via the generalized subadditive functions.
Tingsong Du, Lei Xu
doaj   +1 more source

Some Hermite–Hadamard Type Inequality for the Operator p,P‐Preinvex Function

Journal of Mathematics, Volume 2025, Issue 1, 2025.
The goal of the article is to introduce the operator p,P‐preinvex function and present several features of this function. Also, we establish some Hermite–Hadamard type inequalities for this function.
Mahsa Latifi Moghadam, Omid Pourbahri Rahpeyma, Davood Ebrahimi Bagha, Pramita Mishra   +3 more
wiley   +1 more source