Results 81 to 90 of about 47,370 (280)

Hermite–Hadamard-type inequalities for interval-valued preinvex functions via Riemann–Liouville fractional integrals

Journal of Inequalities and Applications, 2021
In this paper, we introduce ( h 1 , h 2 ) $(h_{1},h_{2})$ -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by using interval-valued Riemann–Liouville fractional integrals.
Nidhi Sharma, Sanjeev Kumar Singh, Shashi Kant Mishra, Abdelouahed Hamdi   +3 more
doaj   +1 more source

Analytic aspects of the dilation inequality for symmetric convex sets in Euclidean spaces [PDF]

arXiv, 2023
We discuss an analytic form of the dilation inequality for symmetric convex sets in Euclidean spaces, which is a counterpart of analytic aspects of Cheeger's isoperimetric inequality. We show that the dilation inequality for symmetric convex sets is equivalent to a certain bound of the relative entropy for symmetric quasi-convex functions, which is ...
arxiv  

An Estimation of Different Kinds of Integral Inequalities for a Generalized Class of Godunova–Levin Convex and Preinvex Functions via Pseudo and Standard Order Relations

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
The connection between generalized convexity and analytic operators is deeply rooted in functional analysis and operator theory. To put the ideas of preinvexity and convexity even closer together, we might state that preinvex functions are extensions of convex functions. Integral inequalities are developed using different types of order relations, each
Zareen A. Khan, Waqar Afzal, Nikhil Khanna   +2 more
wiley   +1 more source

Hermite–Hadamard-type inequalities via n-polynomial exponential-type convexity and their applications

Advances in Difference Equations, 2020
In this paper, we give and study the concept of n-polynomial ( s , m ) $(s,m)$ -exponential-type convex functions and some of their algebraic properties. We prove new generalization of Hermite–Hadamard-type inequality for the n-polynomial ( s , m ) $(s,m)
Saad Ihsan Butt, Artion Kashuri, Muhammad Tariq, Jamshed Nasir, Adnan Aslam, Wei Gao   +5 more
doaj   +1 more source

Generalization of q‐Integral Inequalities for (α, ℏ − m)‐Convex Functions and Their Refinements

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
This article finds q‐ and h‐integral inequalities in implicit form for generalized convex functions. We apply the definition of q − h‐integrals to establish some new unified inequalities for a class of (α, ℏ − m)‐convex functions. Refinements of these inequalities are given by applying a class of strongly (α, ℏ − m)‐convex functions. Several q‐integral
Ria H. Egami, Waseela Bibi, B. A. Younis, Ghulam Farid, Mohammed Ali, Shrideh K. Q. Al-Omari   +5 more
wiley   +1 more source

Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals

Journal of Inequalities and Applications, 2021
In the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals.
Xue-Xiao You, Muhammad Aamir Ali, Hüseyin Budak, Praveen Agarwal, Yu-Ming Chu   +4 more
doaj   +1 more source

Generalization and Refinements of Hermite-Hadamard's Inequality

Rocky Mountain Journal of Mathematics, 2005
In this article, with the help of concept of the harmonic sequence of polynomials, the well known Hermite-Hadamard’s inequality for convex functions is generalied to the cases with bounded derivatives of n-th order, including the so-called n-convex functions, from which Hermite-Hadamard’s inequality is extended and refined.
Qi, Feng, Wei, Zong-Li, Yang, Qiao
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

q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions

Journal of King Saud University: Science, 2018
In this paper, we prove the correct q-Hermite–Hadamard inequality, some new q-Hermite–Hadamard inequalities, and generalized q-Hermite–Hadamard inequality.
Necmettin Alp, Mehmet Zeki Sarıkaya, Mehmet Kunt, İmdat İşcan   +3 more
doaj  

Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex

, 2012
In this article, we extend some estimates of the right-hand side of a Hermite-Hadamard-type inequality for preinvex functions. Then, a generalization to functions of several variables on invex subsets of is introduced.
A. Barani, A. Ghazanfari, S. Dragomir
semanticscholar   +1 more source