Midpoint Type Research Articles

Refinements of some fractional integral inequalities involving extended convex functions and fractional Caputo derivatives

This article examines famous fractional Hermite–Hadamard integral inequalities through the applications of fractional Caputo derivatives and extended convex functions. We develop modifications involving two known classical fractional extended versions of the Hermite–Hadamard type inequalities for the convex function extensions. We also obtain the refinements of some inequalities like Fejér–Hadamard, trapezoidal, and midpoint type for two extended convex functions by applying the Caputo fractional derivative identities. The presented results yield both generalizations and improvements upon previously established inequalities.

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.

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;

A sharp mid-point type inequality

A sharp mid-point type inequality

A STUDY OF FRACTIONAL HERMITE–HADAMARD–MERCER INEQUALITIES FOR DIFFERENTIABLE FUNCTIONS

In this work, we prove a parameterized fractional integral identity involving differentiable functions. Then, we use the newly established identity to establish some new parameterized fractional Hermite–Hadamard–Mercer-type inequalities for differentiable function. The main benefit of the newly established inequalities is that these inequalities can be converted into some new Mercer inequalities of midpoint type, trapezoidal type, and Simpson’s type for differentiable functions. Finally, we show the validation of the results with the help of some mathematical examples and their graphs.

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.

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

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

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

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.

On the generalized Ostrowski type inequalities for co-ordinated convex functions

The purpose of this article is to establish some generalized Ostrowski type inequalities and integral inequalities in the coordinate plane for convex functions of 2 variables. For this, we will specify a generalized identity, and with the help of this integral identity, we will examine the Ostrowski, trapezoid, and midpoint type integral inequalities, including Riemann integral and Riemann-Liouville fractional integral. In this way, we aim to contribute to the generalization of integral inequalities, an important topic in mathematical analysis.

"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."

Parameterized Quantum Fractional Integral Inequalities Defined by Using n-Polynomial Convex Functions

Convexity performs the appropriate role in the theoretical study of inequalities according to the nature and behaviour. There is a strong relation between symmetry and convexity. In this article, we consider a new parameterized quantum fractional integral identity. Following that, our main results are established, which consist of some integral inequalities of Ostrowski and midpoint type pertaining to n-polynomial convex functions. From our main results, we discuss in detail several special cases. Finally, an example and an application to special means of positive real numbers are presented to support our theoretical results.

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

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.

Midpoint type Fractional Integral Inequalities for convex and positive symmetric Increasing functions

: In this study, some midpoint type Hermite-Hadamard fractional integral inequalities and related results for a class of convex functions with respect to an increasing function incorporating a positive-weighted symmetric function generalizing some classical results are discussed.

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.

On Generalization of Different Integral Inequalities for Harmonically Convex Functions

In this study, we first prove a parameterized integral identity involving differentiable functions. Then, for differentiable harmonically convex functions, we use this result to establish some new inequalities of a midpoint type, trapezoidal type, and Simpson type. Analytic inequalities of this type, as well as the approaches for solving them, have applications in a variety of domains where symmetry is important. Finally, several particular cases of recently discovered results are discussed, as well as applications to the special means of real numbers.

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;