Hermite-Hadamard Type Research Articles

Hermite–Hadamard inequalities for Riemann–Liouville fractional integrals

Abstract In this paper, we prove some new inequalities of Hermite–Hadamard type for differentiable functions with h-convex derivatives. It is also shown that the newly established inequalities are extension of the existing inequalities in the literature. Finally, we give applications of the new results and outline some future problems.

Some new integral inequalities for F-convex functions via ABK-fractional operator

In this paper, we present Hermite-Hadamard type and midpoint-type integral inequalities for F-convex function via ABK-fractional integral operators. In the context of differentiable mapping Ψ, we provide multiple new identities and prove new results for F-convex functions using ABK-fractional integral operators whose derivatives in the absolute values are F-convex. We establish correlations between our results and a number of significant results in the literature. The results presented in this paper might encourage more study in this field.

Generalization of quantum calculus and corresponding Hermite–Hadamard inequalities

The aim of this paper is first to introduce generalizations of quantum integrals and derivatives which are called (ϕ-h)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\phi \\,-\\,h)$$\\end{document} integrals and (ϕ-h)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\phi \\,-\\,h)$$\\end{document} derivatives, respectively. Then we investigate some implicit integral inequalities for (ϕ-h)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\phi \\,-\\,h)$$\\end{document} integrals. Different classes of convex functions are used to prove these inequalities for symmetric functions. Under certain assumptions, Hermite–Hadamard-type inequalities for q-integrals are deduced. The results presented herein are applicable to convex, m-convex, and ħ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbar $$\\end{document}-convex functions defined on the non-negative part of the real line.

Generalized Fuzzy-Valued Convexity with Ostrowski’s, and Hermite-Hadamard Type Inequalities over Inclusion Relations and Their Applications

Generalized Fuzzy-Valued Convexity with Ostrowski’s, and Hermite-Hadamard Type Inequalities over Inclusion Relations and Their Applications

Generalised Local Fractional Hermite-Hadamard Type Inequalities on Fractal Sets

Generalised Local Fractional Hermite-Hadamard Type Inequalities on Fractal Sets

Fuzzy Milne, Ostrowski, and Hermite–Hadamard-Type Inequalities for ħ-Godunova–Levin Convexity and Their Applications

In this paper, we establish several Milne-type inequalities for fuzzy number mappings and investigate their relationships with other inequalities. Specifically, we utilize Aumann’s integral and the fuzzy Kulisch–Miranker order, as well as the newly defined class, ħ-Godunova–Levin convex fuzzy number mappings, to derive Ostrowski’s and Hermite–Hadamard-type inequalities for fuzzy number mappings. Using the fuzzy Kulisch–Miranker order, we also establish connections with Hermite–Hadamard-type inequalities. Furthermore, we explore novel ideas and results based on Hermite–Hadamard–Fejér and provide examples and applications to illustrate our findings. Some very interesting examples are also provided to discuss the validation of the main results. Additionally, some new exceptional and classical outcomes have been obtained, which can be considered as applications of our main results.

Quantum symmetric integral inequalities for convex functions

In the context of quantum symmetric calculus, this study proposed more refined version of Ostrowski and Hermite–Hadamard type inequalities. The function involved in these inequalities are convex functions. In order to reach the target, left and right quantum symmetric derivative and corresponding integral are used. Furthermore, the Hölder inequality is established in the frame work of left and right quantum symmetric integral. The new results refined the results about integral inequalities that exist in the literature.

Hermite-Hadamard Inequalities for a New Class of Generalized-(s,m) via Fractional Integral

This paper defines a new generalized (s,m)-σ convex function using the σ convex functions and provides some applications and exact results for this kind of functions. The new definition of the (s,m)-σ convex function class is used to obtain the Hermite Hadamard type integral inequalities existing in the literature, and new integral inequalities are obtained with the help of the σ-Riemann-Liouville fractional integral. Additionally, a new Hermite-Hadamard type fractional integral inequality is constructed using the σ-Riemann-Liouville fractional integral.

Inequalities for strongly s-convex functions via Atangana-Baleanu fractional integral operators

It is more convenient to use fractional derivatives and integrals to express and represent rapid changes than to use integer derivatives and integrals. For this reason, fractional analysis has been found worthy of study in many fields. In recent years, fractional derivatives and integrals have been discussed together with inequality theory and the studies have attracted attention. In this article, we discuss new Hermite-Hadamard type approximations for strongly convex functions with the help of Atangana-Baleanu fractional integral operators. Additionally, new upper bounds have been obtained using various auxiliary inequalities with the help of twice differentiable strongly convex functions.

Hermite–Hadamard type inequality for non-convex functions employing the Caputo–Fabrizio fractional integral

Hermite–Hadamard type inequality for non-convex functions employing the Caputo–Fabrizio fractional integral

Hermite–Hadamard-type inequalities for strongly $$(\alpha ,m)$$-convex functions via quantum calculus

Hermite–Hadamard-type inequalities for strongly $$(\alpha ,m)$$-convex functions via quantum calculus

Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels

Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels

Novel Estimations of Hadamard-Type Integral Inequalities for Raina’s Fractional Operators

In the present paper, utilizing a wide class of fractional integral operators (namely the Raina fractional operator), we develop novel fractional integral inequalities of the Hermite–Hadamard type. With the help of the well-known Riemann–Liouville fractional operators, s-type convex functions are derived using the important results. We also note that some of the conclusions of this study are more reasonable than those found under certain specific conditions, e.g., s=1, λ=α, σ(0)=1, and w=0. In conclusion, the methodology described in this article is expected to stimulate further research in this area.

Some Hermite-Hadamard type integral inequalities for functions whose first derivatives are trigonometrically ρ-convex

Some Hermite-Hadamard type integral inequalities for functions whose first derivatives are trigonometrically ρ-convex

Symmetrical Hermite–Hadamard type inequalities stemming from multiplicative fractional integrals

We firstly study ∗integrability and commutativity for multiplicative fractional integrals with exponential kernels, proposed by Peng et al. (2022). Secondly, making use of such operators, we present a symmetrical multiplicative fractional integrals identity. Based on it, and the fact that the function T∗ is multiplicatively convex or the function (lnT∗)θ is convex for θ>1, especially pondering the case of 0<θ≤1, we establish the symmetrical Hermite–Hadamard type inequalities for multiplicative convexity. We also give some applications in special means under multiplicative calculus.

Analytical properties, fractal dimensions and related inequalities of [formula omitted]-Riemann–Liouville fractional integrals

In this paper, we rigorously explore (k,h)-Riemann–Liouville fractional integrals applied to continuous functions defined on closed real intervals. Firstly, we delve into the analytical properties of (k,h)-Riemann–Liouville fractional integrals for continuous functions, examining aspects like boundedness, continuity, and bounded variation. Secondly, we derive an upper bound for the upper box dimensions of (k,h)-Riemann–Liouville fractional integral graphs for continuous functions defined on real closed intervals. Finally, we present several applications of (k,h)-Riemann–Liouville fractional integral operators, including the reverse analog Hölder inequality, the reverse analog Minkowski inequality, and Hermite–Hadamard-type inequalities.

On the generalization of Hermite-Hadamard type inequalities for [formula omitted]-convex function via fractional integrals

The main motivation in this article is to prove new integral identities and related results. In this paper, we deal with E`-convex function, Hermite-Hadamard type inequalities, and Katugampola fractional integrals. Firstly, we established the Hermite-Hadamard type inequalities for E`-convex function via Katugampola fractional integrals operators. After that we obtain several new identities and give new results of Holder's inequality, Jensen's integral inequality, Young's inequality, and Power mean inequality for E`-convex function by using Katugampola fractional integral operators. We make connections of our results with various results recognized in the literature.

Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$

In this paper, the concept of the $(p,h)$-convex function is introduced, which generalizes the $p$-convex function and the $h$-convex function, and Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$ are established. Furthermore, some mappings related to the above inequalities are studied and some known results are generalized.

A new class of convex functions and applications in entropy and analysis

In this article, we introduce the concepts of k-harmonic mean and k-harmonically convex functions. As an application of k-harmonic mean, we present a model in physics. Also, we prove Jensen type, Hermite–Hadamard type and Mercer type inequalities for these functions. Further, using this results, we give new bounds for Shannon entropy and geometrically mean.

Generalized strongly n-polynomial convex functions and related inequalities

This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite–Hadamard inequality is established for generalized strongly n-polynomial convex functions. Additionally, new integral inequalities of Hermite–Hadamard type are derived for this class of functions using the Hölder–İşcan integral inequality. The results obtained in this paper are compared with those known in the literature, demonstrating the superiority of the new results. Finally, some applications for special means are provided.