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A Note on Characterization of h-Convex Functions via Hermite-Hadamard Type Inequality

Проблемы анализа, 2019
A characterization of h-convex function via Hermite-Hadamard inequality related to the h-convex functions is investigated. In fact it is determined that under what conditions a function is h-convex, if it satisfies the h-convex version of Hermite ...
Delavar M. Rostamian, Dragomir S. S., De La Sen M.   +2 more
doaj   +1 more source

Caputo Fractional Derivative Hadamard Inequalities for Strongly m-Convex Functions

Journal of Function Spaces, 2021
In this paper, two versions of the Hadamard inequality are obtained by using Caputo fractional derivatives and strongly m-convex functions. The established results will provide refinements of well-known Caputo fractional derivative Hadamard inequalities ...
Xue Feng, Baolin Feng, Ghulam Farid, Sidra Bibi, Qi Xiaoyan, Ze Wu   +5 more
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Fractional Refinements of Hermite-Hadamard Type Inequality Involving Mittag-Leffler and Raina's Mappings with Applications to Special Means

Universal Journal of Mathematics and Applications
Fractional integrals have lately become prominent in inequality analysis and have been the focus of several investigations. A new trend in inequality theory has emerged as a result of the investigation of various types of inequality.
Hijaz Ahmad, Muhammad Tariq, Waqar Afzal, Mustafa Bayram, Evren Hincal   +4 more
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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

Generalized Hadamard Fractional Integral Inequalities for Strongly s,m-Convex Functions

Journal of Mathematics, 2021
This article deals with Hadamard inequalities for strongly s,m-convex functions using generalized Riemann–Liouville fractional integrals. Several generalized fractional versions of the Hadamard inequality are presented; we also provide refinements of ...
Chao Miao, Ghulam Farid, Hafsa Yasmeen, Yanhua Bian   +3 more
doaj   +1 more source

New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo–Fabrizio Operator

Fractal and Fractional, 2022
In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type inequality via a new fractional integral operator associated with the Caputo–Fabrizio derivative are presented.
Soubhagya Kumar Sahoo, Pshtiwan Othman Mohammed, Bibhakar Kodamasingh, Muhammad Tariq, Y. S. Hamed   +4 more
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Some Further Results Using Green’s Function for s-Convexity

Journal of Mathematics, 2023
For s-convex functions, the Hermite–Hadamard inequality is already well-known in convex analysis. In this regard, this work presents new inequalities associated with the left-hand side of the Hermite–Hadamard inequality for s-convexity by utilizing a ...
Çetin Yildiz, Levent Akgün, Muhammad Adil Khan, Nasir Rehman   +3 more
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New estimates for Hermite–Hadamard–Fejer-type inequalities containing Raina fractional integrals

Boundary Value Problems
The Hermite–Hadamard–Fejér-type inequality is an effective utensil for examining upper and lower estimations of the integrals of convex functions. In this study, the power mean inequality and Hölder inequality are employed.
Maria Tariq, Ammara Nosheen, Khuram Ali Khan, Khadijah M. Abualnaja   +3 more
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On Upper Estimations of Hermite–Hadamard Inequalities

Mathematics
Convex functions play a key role in many branches of pure and applied mathematics. In this paper, we prove that if a convex function is not continuous, then the classical Hermite–Hadamard inequality, the Hermite–Hadamard inequality for the Riemann ...
Yasin Kaya
doaj   +1 more source

New Integral Inequalities via Generalized Preinvex Functions

Axioms, 2021
The theory of convexity plays an important role in various branches of science and engineering. The objective of this paper is to introduce a new notion of preinvex functions by unifying the n-polynomial preinvex function with the s-type m–preinvex ...
Muhammad Tariq, Asif Ali Shaikh, Soubhagya Kumar Sahoo, Hijaz Ahmad, Thanin Sitthiwirattham, Jiraporn Reunsumrit   +5 more
doaj   +1 more source