Midpoint Type Inequalities Research Articles

Symmetric midpoint type inequalities for (α, m)-Convex Functions with Applications

Symmetric midpoint type inequalities for (α, <i>m</i>)-Convex Functions with Applications

Some Inequalities for Differentiable Functions on a Generalization of Hermite-Hadamard Inequality with Applications

The main identity of midpoint type inequalities is generalized and using this identity some composite midpoint type inequalities are estimated. Moreover, applications to some special means and some error estimates for the composite midpoint formula are discussed.

Hermite –Hadamard and Hermaite –Hadamard Fejer inequality for new f-divergence measure via conformable fractional integrals

In information geometry, a divergence measure is a type of statistical distance and a binary function which established the separation from one probability distribution to another on a statistical numerous. The basic use of divergence measure is statistical data processing, information storage, decision making etc. The most famous inequality regarding the integral mean of a convex function is HermiteâHadamard's inequality and the weighted version of this is called the Hermite-Hadamard-Fejér inequality. Purpose of this paper is to find Hermaite-Hadamard and Hermite-Hadamard Fejer type inequalities for new f-divergence measure with the help of conformable fractional integrals. Hermaite-Hadamard inequality gives us necessary and sufficient condition for a function must be convex. Here we consider the new f-divergence measure, it has the property of convexity. In this research article we drive some inequalities for t-convex function which gives us the extensions of the previous work for convex and t-convex function and also obtains some fractional midpoint type inequalities. The main purpose of this paper is to establish conformal fractional approximation of Hermaite-Hadamard and Hermite-Hadamard Fejer type inequalities for new f-divergence measure which close the fractional integral and the Riemann-Liouville integrable into single form,also gives us some new results for -Riemann-Liouville integral as special cases of main results. This article gives us most useful link between convexity and symmetry.

Hermite-Hadamard type inequalities for new conditions on h-convex functions via ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi $$\\end{document}-Hilfer integral operators

We employ a new function class called B-function to create a new version of fractional Hermite–Hadamard and trapezoid type inequalities on the right-hand side that involves h-convex and ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi $$\\end{document}-Hilfer operators. We also provide new midpoint-type inequalities using h-convex functions.

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 Hermite-Hadamard and midpoint type inequalities in symmetric quantum calculus

&lt;abstract&gt;&lt;p&gt;The Hermite-Hadamard inequalities are common research topics explored in different dimensions. For any interval $ [\mathrm{b_{0}}, \mathrm{b_{1}}]\subset\Re $, we construct the idea of the Hermite-Hadamard inequality, its different kinds, and its generalization in symmetric quantum calculus at $ \mathrm{b_{0}}\in[\mathrm{b_{0}}, \mathrm{b_{1}}]\subset\Re $. We also construct parallel results for the Hermite-Hadamard inequality, its different types, and its generalization on other end point $ \mathrm{b_{1}} $, and provide some examples as well. Some justification with graphical analysis is provided as well. Finally, with the assistance of these outcomes, we give a midpoint type inequality and some of its approximations for convex functions in symmetric quantum calculus.&lt;/p&gt;&lt;/abstract&gt;

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.

New fractional integral inequalities via Euler's beta function

Abstract In this article, we present new fractional integral inequalities via Euler’s beta function in terms of s s -convex mappings. We develop some new generalizations of fractional trapezoid- and midpoint-type inequalities using the class of differentiable s s -convexity. The results obtained in this study extended other related results reported in the literature.

Midpoint-type inequalities via twice-differentiable functions on tempered fractional integrals

In this paper, we obtain an equality involving tempered fractional integrals for twice-differentiable functions. By using this equality, we establish several left Hermite–Hadamard-type inequalities for the case of tempered fractional integrals. Moreover, we derive our results by using special cases of obtained theorems.

A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators

This paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of the obtained identities, we present new trapezoid-type and midpoint-type inequalities via convex functions in the context of the conformable fractional integrals. New inequalities are obtained by taking advantage of the convexity property, power mean inequality, and Hölder’s inequality. We show that this new family of inequalities generalizes some previous research studies by special choices. Furthermore, new other relevant results with trapezoid-type and midpoint-type inequalities are obtained.

Generalized midpoint type inequalities within the $$(\textrm{p,q})$$-calculus framework

Generalized midpoint type inequalities within the $$(\textrm{p,q})$$-calculus framework

Generalized fractional midpoint type inequalities for co-ordinated convex functions

In this research paper, we investigate generalized fractional integrals to obtain midpoint type inequalities for the co-ordinated convex functions. First of all, we establish an identity for twice partially differentiable mappings. By utilizing this equality, some midpoint type inequalities via generalized fractional integrals are proved. We also show that the main results reduce some midpoint inequalities given in earlier works for Riemann integrals and Riemann-Liouville fractional integrals. Finally, some new inequalities for k-Riemann-Liouville fractional integrals are presented as special cases of our results.

A new q-Hermite-Hadamard's inequality and estimates for midpoint type inequalities for convex functions

A new q-Hermite-Hadamard's inequality and estimates for midpoint type inequalities for convex functions

"On the generalized trapezoid and midpoint type inequalities involving Euler's beta function}"

"The main object of this paper is to present some generalizations of fractional integral inequalities involving Euler's beta function of Hermite-Hadamard type which cover the previously published result such as Riemann integral, Riemann-Liouville fractional integral, k-Riemann-Liouville fractional integral."

A Note on Fractional Midpoint Type Inequalities for Co-ordinated (s1, s2)-Convex Functions

In the present paper, some Hermite-Hadamard type inequalities in the case of differentiable co-ordinated (s_1," " s_2)-convex functions are investigated. Namely, the generalizations of the midpoint type inequalities in the case of differentiable co-ordinated (s_1," " s_2)-convex functions in the second sense on the rectangle from the plain are established. In addition to this, it is presented several inequalities to the case of Riemann-Liouville fractional integrals and k-Riemann-Liouville fractional integrals by choosing the special cases of our obtained main results

Further Midpoint Inequalities via Generalized Fractional Operators in Riemann–Liouville Sense

In this study, new midpoint-type inequalities are given through recently generalized Riemann–Liouville fractional integrals. Foremost, we present an identity for a class of differentiable functions including the proposed fractional integrals. Then, several midpoint-type inequalities containing generalized Riemann–Liouville fractional integrals are proved by employing the features of convex and concave functions. Furthermore, all obtained results in this study can be compared to previously published results.

Quantum analog of some trapezoid and midpoint type inequalities for convex functions

In this paper a new quantum analog of Hermite-Hadamard inequality is presented, and based on it, two new quantum trapezoid and midpoint identities are obtained. Moreover, the quantum analog of some trapezoid and midpoint type inequalities are established.

Positive Weighted Symmetry Function Kernels and Some Related Inequalities for a Generalized Class of Convex Functions

The fractional integral inequalities are crucial to deal applied problems. The present paper deals with the generalize midpoint type inequalities for a certain class of convex functions, namely, MT-convex functions in the setting of weighted fractional integral. It can be observed from the remarks given in the paper that our results or more generalized than existing results of literature and many of them can be obtained immediately from our results.

Certain inequalities in frame of the left-sided fractional integral operators having exponential kernels

&lt;abstract&gt;&lt;p&gt;By virtue of the left-sided fractional integral operators having exponential kernels, proposed by Ahmad et al. in [J. Comput. Appl. Math. 353:120-129, 2019], we create the left-sided fractional Hermite–Hadamard type inequalities for convex mappings. Moreover, to study certain fractional trapezoid and midpoint type inequalities via the differentiable convex mappings, two fractional integral identities are proven. Also, we show the important connections of the derived outcomes with those classical integrals clearly. Finally, we provide three numerical examples to verify the correctness of the presented inequalities that occur with the variation of the parameter $ \mu $.&lt;/p&gt;&lt;/abstract&gt;

Certain exponential type $ m $-convexity inequalities for fractional integrals with exponential kernels

&lt;abstract&gt;&lt;p&gt;By applying exponential type $ m $-convexity, the Hölder inequality and the power mean inequality, this paper is devoted to conclude explicit bounds for the fractional integrals with exponential kernels inequalities, such as right-side Hadamard type, midpoint type, trapezoid type and Dragomir-Agarwal type inequalities. The results of this study are obtained for mappings $ \omega $ where $ \omega $ and $ |\omega'| $ (or $ |\omega'|^q $with $ q\geq 1 $) are exponential type $ m $-convex. Also, the results presented in this article provide generalizations of those given in earlier works.&lt;/p&gt;&lt;/abstract&gt;