Results 11 to 20 of about 252 (113)

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
doaj   +2 more sources

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

Journal of Mathematics
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.
Muhammad Zafran, Muhammad Adil Khan, Tahir Ullah Khan, Božidar Ivanković, Z. M. M. M. Sayed, Mohamed Sharaf   +5 more
doaj   +2 more sources

Exponentially Convex Functions on the Coordinates and Novel Estimations via Riemann‐Liouville Fractional Operator

Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023
In this study, the modification of the concept of exponentially convex function, which is a general version of convex functions, given on the coordinates, is recalled. With the help of an integral identity which includes the Riemann‐Liouville (RL) fractional integral operator, new Hadamard‐type inequalities are proved for exponentially convex functions
Ahmet Ocak Akdemir, Sinan Aslan, Mustafa Ali Dokuyucu, Ercan Çelik, Serena Matucci   +4 more
wiley   +1 more source

Estimations of the Slater Gap via Convexity and Its Applications in Information Theory

Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022
Convexity has played a prodigious role in various areas of science through its properties and behavior. Convexity has booked record developments in the field of mathematical inequalities in the recent few years. The Slater inequality is one of the inequalities which has been acquired with the help of convexity.
Muhammad Adil Khan, Hidayat Ullah, Tareq Saeed, Hamed H. Alsulami, Z. M. M. M. Sayed, Ahmed Mohammed Alshehri, Fahd Jarad   +6 more
wiley   +1 more source

Some Improvements of Jensen’s Inequality via 4‐Convexity and Applications

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
The intention of this note is to investigate some new important estimates for the Jensen gap while utilizing a 4‐convex function. We use the Jensen inequality and definition of convex function in order to achieve the required estimates for the Jensen gap.
Hidayat Ullah, Muhammad Adil Khan, Tareq Saeed, Zaid Mohammed Mohammed Mahdi Sayed, Sarfraz Nawaz Malik   +4 more
wiley   +1 more source

Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
The main objective of this article is to introduce the notion of n–polynomial harmonically tgs–convex function and study its algebraic properties. First, we use this notion to present new variants of the Hermite–Hadamard type inequality and related integral inequalities, as well as their fractional analogues.
Artion Kashuri, Soubhagya Kumar Sahoo, Bibhakar Kodamasingh, Muhammad Tariq, Ahmed A. Hamoud, Homan Emadifar, Faraidun K. Hamasalh, Nedal M. Mohammed, Masoumeh Khademi, Guotao Wang   +9 more
wiley   +1 more source

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
doaj   +1 more source

Some Novel Estimates of Hermite–Hadamard and Jensen Type Inequalities for (h1,h2)-Convex Functions Pertaining to Total Order Relation [PDF]

, 2022
There are different types of order relations that are associated with interval analysis for determining integral inequalities. The purpose of this paper is to connect the inequalities terms to total order relations, often called (CR)-order.
Afzal, Waqar, De la Sen Parte, Manuel, Saeed, Tareq, Shabbir, Khurram, Treanţă, Savin   +4 more
core   +3 more sources

(p, h)‐Convex Functions Associated with Hadamard and Fejér‐Hadamard Inequalities via k‐Fractional Integral Operators

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
In this article, generalized versions of the k‐fractional Hadamard and Fejér‐Hadamard inequalities are constructed. To obtain the generalized versions of these inequalities, k‐fractional integral operators including the well‐known Mittag‐Leffler function are utilized.
Xiujun Zhang, Ghulam Farid, Ayşe Kübra Demirel, Chahn Yong Jung, Muhammad Arif   +4 more
wiley   +1 more source

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
doaj   +1 more source