Hermite-Hadamard Inequalities Research Articles

New Midpoint-type Inequalities of Hermite-Hadamard Inequality with Tempered Fractional Integrals

In this research, we get some midpoint type inequalities of Hermite-Hadamard inequality via tempered fractional integrals. For this, we first obtain an identity. After that, using this identity and with the help of modulus function, Hölder inequality, power mean inequality, ongoing research and the papers mentioned, we have reached our intended midpoint type inequalities. Also, we give the special cases of our results. We see that our special results give earlier works.

More Correct Berezin Symbol Inequalities

The purpose of this research is to show bounds for some Berezin number inequalities in an innovative approach. Some inequalities have been proven using the improvement of the Hermite-Hadamard inequality. These inequalities are a refined version of Huban et al.'s inequalities (Huban et al., 2021b; Huban et al., 2022a) and Başaran et al.'s inequalities (Başaran et al., 2022). Finally, we prove last three theorems by applying the method of Cartesian decomposition.

Generalization of Hermite-Hadamard Inequality for Twice Differentiable Convex and Quasi-Convex Functions

Generalization of Hermite-Hadamard Inequality for Twice Differentiable Convex and Quasi-Convex Functions

On Inequalities for q - h -Integrals via Convex Functions

This article aims to investigate unified versions of the well-known Hermite–Hadamard inequality by considering q - h -integrals and properties of convex functions. Currently published results for q -integrals can be deduced from inequalities of this paper. Moreover, some new results are presented in terms of corollaries.

Some Refinements of the Hermite–Hadamard Inequality with the Help of Weighted Integrals

Some Refinements of the Hermite–Hadamard Inequality with the Help of Weighted Integrals

A modified class of Ostrowski-type inequalities and error bounds of Hermite–Hadamard inequalities

This paper aims to extend the application of the Ostrowski inequality, a crucial tool for figuring out the error bounds of various numerical quadrature rules, including Simpson’s, trapezoidal, and midpoint rules. Specifically, we develop a more comprehensive class of Ostrowski-type inequalities by utilizing the weighted version of Riemann–Liouville (RL) fractional integrals on an increasing function. We apply our findings to estimate the error bounds of Hadamard-type inequalities. Our results are more comprehensive, since we obtain the results of the existing literatures as particular cases for certain parameter values. This research motivates researchers to apply this concept to other fractional operators.

New Fractional Integral Inequalities via k-Atangana–Baleanu Fractional Integral Operators

We propose the definitions of some fractional integral operators called k-Atangana–Baleanu fractional integral operators. These newly proposed operators are generalizations of the well-known Atangana–Baleanu fractional integral operators. As an application, we establish a generalization of the Hermite–Hadamard inequality. Additionally, we establish some new identities involving these new integral operators and obtained new fractional integral inequalities of the midpoint and trapezoidal type for functions whose derivatives are bounded or convex.

Sharpening celebrated convex inequalities with applications to operators and entropies

The Jensen, Jensen–Mercer, and Hermite–Hadamard inequalities have been key in advancing convex inequalities for scalars and operators, with several applications in fields like mathematical physics, operator theory and mathematical inequalities. This paper presents a new argument leading to interesting refinements of these celebrated inequalities. Applications that include entropy and operator inequalities will be presented.

Hermite-Hadamard inequalities for quantum integrals: A unified approach

Let s0 be a fixed point of a strictly increasing continuous function β. Hamza et al. introduced the quantum operator Dβ[g](θ):=g(β(θ))−g(θ)β(θ)−θ, θ≠s0 and Dβ[g](s0):=g′(s0) if θ=s0. For specific choices of the function β one obtains the known Jackson q-operator Dq as well as the Hahn quantum operator Dq,ω. Regarding its inverse operator, the β-integral, we establish the corresponding β-Hermite-Hadamard inequalities. Among others, we also obtain the Hermite-Hadamard type inequalities for the Jackson q-integral, the Nörlund integral and for the Jackson-Thomae (or Jackson-Nörlund) q,ω-integral.

A Note on the New Ostrowski and Hadamard Type Inequalities via the Hölder–İşcan Inequality

For all convex functions, the Hermite–Hadamard inequality is already well known in convex analysis. In this regard, Hermite–Hadamard and Ostrowski type inequalities were obtained using exponential type convex functions in this work. In addition, new generalizations were found for different values of θ. In conclusion, we believe that our work’s technique will inspire more study in this field.

New quantum Hermite–Hadamard-type inequalities for p -convex functions involving recently defined quantum integrals

UDC 517.5 We develop new Hermite–Hadamard-type integral inequalities for p -convex functions in the context of q -calculus by using the concept of recently defined T q -integrals. Then thе obtained Hermite–Hadamard inequality for p -convex functions is used to get new Hermite–Hadamard inequality for coordinated p -convex functions. Furthermore, we present some examples to demonstrate the validity of our main results. We hope that the ideas and techniques of this study may stimulate further research in this field.

Innovative Interpolating Polynomial Approach to Fractional Integral Inequalities and Real-World Implementations

Our paper explores Hermite–Hadamard inequalities through the application of Abel–Gontscharoff Green’s function methodology, which involves interpolating polynomials and Riemann-type generalized fractional integrals. While establishing our main results, we explore new identities. These identities are used to estimate novel findings for functions, such that the second derivative of the functions is monotone, absolutely convex, and concave. A section relating the results of exploration to generalized means and trapezoid formulas is included in the applications. We anticipate that the method presented in this study will inspire further research in this field.

On Hermite-Hadamard-Type Inequalities for Subharmonic Functions Over Circular Ring Domains

In this note, we study the so-called Hermite-Hadamard inequality for the class of subharmonic functions. We first prove an inequality of this type for subharmonic functions over circular ring domains. Next, a new Hermite-Hadamard-type inequality over a disk is deduced. Moreover, we introduce the class of subharmonic functions on the coordinates, which includes the class of convex functions on the coordinates, and establish several new integral inequalities for this class of functions over various product domains: product of disks, product of circular rings and product of a disk and a circular ring.

Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr-h-Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings

The application of fractional calculus to interval analysis is vital for the precise derivation of integral inequalities on set-valued mappings. The objective of this article is to reformulated the well-known Hermite–Hadamard inequality into various new variants via fractional integral operator (Riemann–Liouville) and generalize the various previously published results on set-valued mappings via center and radius order relations using harmonical h-convex functions. First, using these notions, we developed the Hermite–Hadamard (H–H) inequality, and then constructed some product form of these inequalities for harmonically convex functions. Moreover, to demonstrate the correctness of these results, we constructed some interesting non-trivial examples.

Hermite–Hadamard type inequalities for multiplicatively harmonic convex functions

In this work, the notion of a multiplicative harmonic convex function is examined, and Hermite–Hadamard inequalities for this class of functions are established. Many inequalities of Hermite–Hadamard type are also taken into account for the product and quotient of multiplicative harmonic convex functions. In addition, new multiplicative integral-based inequalities are found for the quotient and product of multiplicative harmonic convex and harmonic convex functions. In addition, we provide certain upper limits for such classes of functions. The obtained results have been verified by providing examples with included graphs. The findings of this study may encourage more research in several scientific areas.

Hermite–Hadamard-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Godunova–Levin and (h1, h2)-Convex Functions

This note generalizes several existing results related to Hermite–Hadamard inequality using h-Godunova–Levin and (h1,h2)-convex functions using a fractional integral operator associated with the Caputo–Fabrizio fractional derivative. This study uses a non-singular kernel and constructs some new theorems associated with fractional order integrals. Furthermore, we demonstrate that the obtained results are a generalization of the existing ones. To demonstrate the correctness of these results, we developed a few interesting non-trivial examples. Finally, we discuss some applications of our findings associated with special means.

On Hardy and Hermite-Hadamard inequalities for $N$-tuple diamond-alpha integral

In this paper, we aim to construct $n$ dimensional Jensen, Hardy and Hermite-Hadamard type inequalities for multiple diamond-alpha integral on time scales. The cases of Hardy type inequality with a weighted function and Hermite-Hadamard type inequality with three variables are also considered minutely.

Hermite-Hadamard Inequalities Type Using Fractional Integrals for MT-convex Stochastic Process

By applying the standard fractional integral operator of Riemann-Liouville on MT-convex stochastic processes, we can obtain new inequalities of Hermite-Hadamard, providing in the process new estimates on these types of Hermite-Hadamard inequalities for stochastic process whose first derivatives absolute values are MT-convex.

Fejér-Type Inequalities for Some Classes of Differentiable Functions

We let υ be a convex function on an interval [ι1,ι2]⊂R. If ζ∈C([ι1,ι2]), ζ≥0 and ζ is symmetric with respect to ι1+ι22, then υ12∑j=12ιj∫ι1ι2ζ(s)ds≤∫ι1ι2υ(s)ζ(s)ds≤12∑j=12υ(ιj)∫ι1ι2ζ(s)ds. The above estimates were obtained by Fejér in 1906 as a generalization of the Hermite–Hadamard inequality (the above inequality with ζ≡1). This work is focused on the study of right-side Fejér-type inequalities in one- and two-dimensional cases for new classes of differentiable functions υ. In the one-dimensional case, the obtained results hold without any symmetry condition imposed on the weight function ζ. In the two-dimensional case, the right side of Fejer’s inequality is extended to the class of subharmonic functions υ on a disk.

Weighted Hermite-Hadamard inequalities for r-times differentiable preinvex functions for k-fractional integrals

Abstract In this article, we have established some new bounds of Fejér-type Hermite-Hadamard inequality for k k -fractional integrals involving r r -times differentiable preinvex functions. It is noteworthy that in the past, there was no weighted version of the left and right sides of the Hermite-Hadamard inequality for k k -fractional integrals for generalized convex functions available in the literature.