Results 61 to 70 of about 250 (112)

Integral inequalities of Hermite-Hadamard type via $ q-h $ integrals [PDF]

, 2023
The well-known Hermite-Hadamard inequality for convex functions is extensively studied for different kinds of integrals and derivatives. This paper investigates some of its variants for $ q-h $-integrals using properties of convex functions. Inequalities
Dong Chen, Ghulam Farid, Matloob Anwar, Waseela Bibi   +3 more
core   +1 more source

A Fractal Approach to Hermite–Hadamard Type Inequalities via Generalized Beta Function

Journal of Mathematics, Volume 2025, Issue 1, 2025.
The main aim of this manuscript is to explore the connection between fractal geometry and convexity, highlighting the mathematical appeal of fractals. Using the beta function, we introduce a new class of generalized Hermite–Hadamard (HH) type inequalities.
Saad Ihsan Butt, Muhammad Mehtab, Youngsoo Seol, Mohammad W. Alomari   +3 more
wiley   +1 more source

Exploring Advanced Versions of Hermite‐Hadamard and Trapezoid‐Type Inequalities by Implementation of Fuzzy Interval‐Valued Functions

Journal of Function Spaces, Volume 2024, Issue 1, 2024.
The extension of interval‐valued and real‐valued functions known as fuzzy interval‐valued function (FIVF) has made substantial contributions to the theory of interval analysis. In this article, we explore the importance of h‐Godunova‐Levin fuzzy convex and preinvex functions and also develop the new generation of the Hermite‐Hadamard and trapezoid‐type
Yaqun Niu, Rana Safdar Ali, Naila Talib, Shahid Mubeen, Gauhar Rahman, Çetin Yildiz, Fuad A. Awwad, Emad A. A. Ismail, Wilfredo Urbina   +8 more
wiley   +1 more source

Advanced Hermite-Hadamard-Mercer Type Inequalities with Refined Error Estimates and Applications

Fractal and Fractional
The purpose of this research is to develop a set of Hermite–Hadamard–Mercer-type inequalities that involve different types of fractional integral operators such as classical Riemann–Liouville fractional integral operators.
Arslan Munir, Hüseyin Budak, Artion Kashuri, Loredana Ciurdariu   +3 more
doaj   +1 more source

New fractional estimates for Hermite-Hadamard-Mercer’s type inequalities

Alexandria Engineering Journal, 2020
An analogous version of Hermite-Hadamard-Mercer’s inequality has been established using the Katugampola fractional integral operators. The result is the generalization of the Riemann-Liouville fractional integral operator combined with the left and right
Hong-Hu Chu, Saima Rashid, Zakia Hammouch, Yu-Ming Chu   +3 more
doaj   +1 more source

Hermite–Hadamard–Mercer-Type Inequalities for Three-Times Differentiable Functions

Axioms
In this study, an integral identity is given in order to present some Hermite–Hadamard–Mercer-type inequalities for functions whose powers of the absolute values of the third derivatives are convex. Several consequences and three applications to special means are given, as well as four examples with graphics which illustrate the validity of the results.
Loredana Ciurdariu, Eugenia Grecu
openaire   +2 more sources

Hermite–Jensen–Mercer type inequalities for conformable integrals and related results

Advances in Difference Equations, 2020
In this paper, certain Hermite–Jensen–Mercer type inequalities are proved via conformable integrals of arbitrary order. We establish some different and new fractional Hermite–Hadamard–Mercer type inequalities for a differentiable function f whose ...
Saad Ihsan Butt, Mehroz Nadeem, Shahid Qaisar, Ahmet Ocak Akdemir, Thabet Abdeljawad   +4 more
doaj   +1 more source

New Hermite–Jensen–Mercer-type inequalities via k-fractional integrals

Advances in Difference Equations, 2020
In the article, we establish serval novel Hermite–Jensen–Mercer-type inequalities for convex functions in the framework of the k-fractional conformable integrals by use of our new approaches.
Saad Ihsan Butt, Muhammad Umar, Saima Rashid, Ahmet Ocak Akdemir, Yu-Ming Chu   +4 more
doaj   +1 more source

A version of Hermite-Hadamard-Mercer inequality and associated results

Ain Shams Engineering Journal
Over the past decade, the Hermite-Hadamard inequality has attracted significant attention from mathematicians, leading to the development of various extensions and generalizations involving different fractional operators, stochastic processes ...
Zhenglin Zhang, Muhammad Adil Khan, Jamroz Khan, Shah Faisal, Xuewu Zuo, Mohammed Kbiri Alaoui   +5 more
doaj   +1 more source

Some Hermite–Jensen–Mercer type inequalities for k-Caputo-fractional derivatives and related results

Advances in Difference Equations, 2020
In this paper, certain Hermite–Hadamard–Mercer type inequalities are proved via k-Caputo fractional derivatives. We established some new k-Caputo fractional derivatives inequalities with Hermite–Hadamard–Mercer type inequalities for differentiable ...
Shupeng Zhao, Saad Ihsan Butt, Waqas Nazeer, Jamshed Nasir, Muhammad Umar, Ya Liu   +5 more
doaj   +1 more source