Results 31 to 40 of about 264 (118)

The Hermite–Hadamard–Jensen–Mercer Type Inequalities for Riemann–Liouville Fractional Integral [PDF]

Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021
In this paper, we give Hermite–Hadamard type inequalities of the Jensen–Mercer type for Riemann–Liouville fractional integrals. We prove integral identities, and with the help of these identities and some other eminent inequalities, such as Jensen, Hölder, and power mean inequalities, we obtain bounds for the difference of the newly obtained ...
Hua Wang, Jamroz Khan, Muhammad Adil Khan, Sadia Khalid, Rewayat Khan   +4 more
openalex   +2 more sources

A New Inclusion on Inequalities of the Hermite–Hadamard–Mercer Type for Three-Times Differentiable Functions

Mathematics
The goal of this study is to develop numerous Hermite–Hadamard–Mercer (H–H–M)-type inequalities involving various fractional integral operators, including classical, Riemann–Liouville (R.L), k-Riemann–Liouville (k-R.L), and their generalized fractional ...
Talib Hussain, Loredana Ciurdariu, Eugenia Grecu   +2 more
doaj   +2 more sources

POST-QUANTUM HERMITE-JENSEN-MERCER INEQUALITIES [PDF]

, 2023
The Jensen-Mercer inequality, which is well known in the literature, has an important place in mathematics and related disciplines. In this work, we obtain the Hermite-Jensen-Mercer inequality for post-quantum integrals by utilizing Jensen-Mercer ...
Bohner, Martin, Budak, Hüseyin, Kara, Hasan   +2 more
core   +5 more sources

On Ostrowski–Mercer’s Type Fractional Inequalities for Convex Functions and Applications [PDF]

, 2023
This research focuses on the Ostrowski–Mercer inequalities, which are presented as variants of Jensen’s inequality for differentiable convex functions. The main findings were effectively composed of convex functions and their properties. The results were
Aljuaid, Munirah, De la Sen Parte, Manuel, Kashuri, Artion, Mishra, Soumyarani, Sahoo, Soubhagya Kumar   +4 more
core   +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

Generalized Fractal Jensen–Mercer and Hermite–Mercer type inequalities via h-convex functions involving Mittag–Leffler kernel

Alexandria Engineering Journal, 2022
In this paper, we present generalized Jensen-Mercer inequality for a generalized h-convex function on fractal sets. We proved Hermite-Hadamard-Mercer local fractional integral inequalities via integral operators pertaining Mittag-Leffler kernel. Also, we
Peng Xu, Saad Ihsan Butt, Saba Yousaf, Adnan Aslam, Tariq Javed Zia   +4 more
doaj   +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 variants on Mercer's Hermite-Hadamard like inclusions of interval-valued functions for strong Kernel

AIMS Mathematics, 2023
Using Atangana-Baleanu (AB) fractional integral operators, we first establish some fractional Hermite-Hadamard-Mercer inclusions for interval-valued functions in this study.
Jamshed Nasir , Saber Mansour, Shahid Qaisar, Hassen Aydi   +3 more
doaj   +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