Hermite-Hadamard Type Inequalities Research Articles

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

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.

On a new version of Hermite–Hadamard-type inequality based on proportional Caputo-hybrid operator

In mathematics and the applied sciences, as a very useful tool, fractional calculus is a basic concept. Furthermore, in many areas of mathematics, it is better to use a new hybrid fractional operator, which combines the proportional and Caputo operators. So we concentrate on the proportional Caputo-hybrid operator because of its numerous applications. In this research, we introduce a novel extension of the Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator and establish an identity. Then, taking into account this novel generalized identity, we develop some integral inequalities associated with the left-side of Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator. Moreover, to illustrate the newly established inequalities, we give some examples with the help of graphs.

Refinements and Applications of Hermite–Hadamard-Type Inequalities Using Hadamard Fractional Integral Operators and GA-Convexity

Refinements and Applications of Hermite–Hadamard-Type Inequalities Using Hadamard Fractional Integral Operators and GA-Convexity

Fractional Mercer's Hermite–Hadamard type inequalities in the frame of interval analysis and its applications to matrix

Fractional Mercer's Hermite–Hadamard type inequalities in the frame of interval analysis and its applications to matrix

New Developments of Hermite–Hadamard Type Inequalities via s-Convexity and Fractional Integrals

In this paper, we present an identity for differentiable functions that has played an important role in proving Hermite–Hadamard type inequalities for functions whose absolute values of first derivatives are s-convex functions. Meanwhile, some Hermite–Hadamard type inequalities for the functions whose absolute values of second derivatives are s-convex are also established with the help of an existing identity in literature. Many limiting results are deduced from the main results which are stated in remarks. Some applications of proved results are also discussed in the present study.

New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator

Fractional calculus is a crucial foundation in mathematics and applied sciences, serving as an extremely valuable tool. Besides, the new hybrid fractional operator, which combines proportional and Caputo operators, offers better applications in numerous fields of mathematics and computer sciences. Due to its wide range of applications, we focus on the proportional Caputo-hybrid operator in this research article. Firstly, we begin by establishing a novel identity for this operator. Then, based on the newfound identity, we establish some integral inequalities that are relevant to the left-hand side of Hermite–Hadamard-type inequalities for the proportional Caputo-hybrid operator. Furthermore, we show how the results improve upon and refine many previous findings in the setting of integral inequalities. Later, we present specific examples together with their related graphs to offer a better understanding of the newly obtained inequalities. Our results not only extend previous studies but also provide valuable viewpoints and methods for tackling a wide range of mathematical and scientific problems.

Some novel inequalities for Caputo Fabrizio fractional integrals involving ( α , s ) -convex functions with applications

ABSTRACT Fractional calculus is extremely important and should not be undervalued due to its critical role in the theory of inequalities. In this article, different generalized Hermite-Hadamard type inequalities for functions whose modulus of first derivatives are ( α , s ) -convex are presented, via Caputo-Fabrizio integrals. Graphical justifications of main results are presented. Graphs enable us to support our conclusions and show the reliability of our findings. Additionally, some applications to probability theory and numerical integration are also established. As special cases, certain established outcomes from different articles are recaptured. This study acts as a stimulant for future studies, inspiring researchers to investigate more thorough results by utilizing generalized fractional operators and broadening the idea of convexity.

On some new and general q-Hermite–Hadamard type inequalities for convex functions

In this paper, we establish a new version of Hermite–Hadamard type inequality for convex functions. Moreover, we establish a general version of q-integral identity involving q-differentiable functions to prove some new q-midpoint and q-trapezoidal type inequalities for q-differentiable convex functions. It is also shown that the newly established inequalities can be converted into some existing inequalities within the literature. Finally, we add some mathematical examples to show the validation of newly established inequalities.

On Hermite-Hadamard type inequalities for co-ordinated convex function via conformable fractional integrals

&lt;abstract&gt;&lt;p&gt;In this study, some new Hermite-Hadamard type inequalities for co-ordinated convex functions were obtained with the help of conformable fractional integrals. We have presented some remarks to give the relation between our results and earlier obtained results. Moreover, an identity for partial differentiable functions has been established. By using this equality and concept of co-ordinated convexity, we have proven a trapezoid type inequality for conformable fractional integrals.&lt;/p&gt;&lt;/abstract&gt;

INEQUALITIES FOR STRONGLY r-CONVEX FUNCTIONS ON TIME SCALES

In this paper, first we establish the Hermite-Hadamard type inequality based on diamond-α integral for a subset of strongly r-convex functions. Then we prove several new inequalities for n-times continuously differentiable strongly r-convex functions on time scales by virtue of some techniques and introducing new quantities.

Conformable fractional Hermite-Hadamard type inequalities for functions whose derivatives are s-preinvex

In this paper, we establish a new integral identity, based on this identity, we derive some new conformable fractional Hermite-Hadamard type inequalities for functions whose first derivatives are s-preinvex in the second sense.

Some k-Fractional Integral Inequalities for p-Convex Functions

In this paper, we use Riemann-Liouville k-fractional and k-fractional confomable integrals to prove Hermite-Hadamard inequality, an identity and Hermite-Hadamard type inequality for p-convex functions. Some special cases are also discussed. Our work is extensions of other related previous results.

Counter-examples to Breckner-convexity

In this paper, we examine convexity type inequalities. Let D be a nonempty convex subset of a linear space, c&gt;0 and α:D-D→R be a given even function. The inequality f((x+y)/2) ≤ c f(x) + c f(y) + α(x-y) (x,y € D) is the focus of our examinations. We will construct an example to show that for c=1, this Jensen type inequality does not imply the convexity of the function. Then, we compare this inequality with Hermite–Hadamard type inequalities.

Inequalities for fractional integral with the use of stochastic orderings

In this paper, we show the connections of inequalities involving fractional integrals with Ohlin lemma and Levin-Stechkin theorem. First, we give a new proof of the fractional version of the inequality of Hermite Hadamard type and then we extend it in two directions. Thus we compare the fractional expression occurring in this inequality with the usual integral and we obtain stronger inequalities (one of them is related to Bullen inequality).

Hermite-Hadamard type inequalities via weighted integral operators

In this paper, we consider general convex functions of various type. We establish some new integral inequalities of Hermite-Hadamard type for (h, s, m)-convex and (h, m)-convex functions, using generalized integrals. We also investigate differentiable functions with general convex derivative. The proven results generalize many results previously known from the literature.