Results 21 to 30 of about 558,085 (88)

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

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

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

New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function

Journal of Function Spaces, 2021
In 2003, Mercer presented an interesting variation of Jensen’s inequality called Jensen–Mercer inequality for convex function. In the present paper, by employing harmonically convex function, we introduce analogous versions of Hermite–Hadamard ...
Saad Ihsan Butt, Saba Yousaf, Atifa Asghar, Khuram Ali Khan, Hamid Reza Moradi   +4 more
doaj   +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

New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators

Journal of Mathematics, 2020
In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators ...
Qiong Kang, Saad Ihsan Butt, Waqas Nazeer, Mehroz Nadeem, Jamshed Nasir, Hong Yang   +5 more
doaj   +1 more source

New conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in terms of generalized conformable fractional operators via majorization

Demonstratio Mathematica, 2023
The Hermite-Hadamard inequality is regarded as one of the most favorable inequalities from the research point of view. Currently, mathematicians are working on extending, improving, and generalizing this inequality.
Saeed Tareq, Khan Muhammad Adil, Faisal Shah, Alsulami Hamed H., Alhodaly Mohammed Sh.   +4 more
doaj   +1 more source

(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