scholarly journals New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Qiong Kang ◽  
Saad Ihsan Butt ◽  
Waqas Nazeer ◽  
Mehroz Nadeem ◽  
Jamshed Nasir ◽  
...  
Keyword(s):  
Fractional Integral ◽  
Hölder’S Inequality ◽  
Integral Operators ◽  
Differentiable Mapping ◽  
Fractional Integral Operators ◽  
Hölder's Inequality ◽  
Differentiable Functions ◽  
New Variant ◽  
The Absolute

In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators by utilizing Jensen–Mercer inequality for differentiable mapping ϒ whose derivatives in the absolute values are convex. Moreover, we construct new lemmas for differentiable functions ϒ′, ϒ″, and ϒ‴ and formulate related inequalities for these differentiable functions using variants of Hölder’s inequality.

scholarly journals k -Fractional Variants of Hermite-Mercer-Type Inequalities via s -Convexity with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Saad Ihsan Butt ◽  
Jamshed Nasir ◽  
Shahid Qaisar ◽  
Khadijah M. Abualnaja
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Special Functions ◽  
Integral Operators ◽  
The Novel ◽  
Differentiable Mapping ◽  
Real Numbers ◽  
Fractional Integral Operators ◽  
Special Means ◽  
The Absolute

This article is aimed at studying novel generalizations of Hermite-Mercer-type inequalities within the Riemann-Liouville k -fractional integral operators by employing s -convex functions. Two new auxiliary results are derived to govern the novel fractional variants of Hadamard-Mercer-type inequalities for differentiable mapping Ψ whose derivatives in the absolute values are convex. Moreover, the results also indicate new lemmas for Ψ ′ , Ψ ′ ′ , and Ψ ′ ′ ′ and new bounds for the Hadamard-Mercer-type inequalities via the well-known Hölder’s inequality. As an application viewpoint, certain estimates in respect of special functions and special means of real numbers are also illustrated to demonstrate the applicability and effectiveness of the suggested scheme.

scholarly journals Certain Chebyshev-Type Inequalities Involving Fractional Conformable Integral Operators

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 364 ◽  
Author(s):  
Gauhar Rahman ◽  
Zafar Ullah ◽  
Aftab Khan ◽  
Erhan Set ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Differentiable Functions ◽  
New Variant

Since an interesting functional by P.L. Chebyshev was presented in the year 1882, many results, which are called Chebyshev-type inequalities, have been established. Some of these inequalities were obtained by using fractional integral operators. Very recently, a new variant of the fractional conformable integral operator was introduced by Jarad et al. Motivated by this operator, we aim at establishing novel inequalities for a class of differentiable functions, which are associated with Chebyshev’s functional, by employing a fractional conformable integral operator. We also aim at showing important connections of the results here with those including Riemann–Liouville fractional and classical integrals.

scholarly journals On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Havva Kavurmacı Önalan ◽  
Ahmet Ocak Akdemir ◽  
Merve Avcı Ardıç ◽  
Dumitru Baleanu
Keyword(s):  
Integral Equation ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Frequency Of Use ◽  
Second Derivatives ◽  
New Variant ◽  
Type Integral ◽  
Basic Concepts

AbstractThe main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new variant of Hermite–Hadamard (HH-) inequality is obtained for s-convex functions in the second sense. Then, an integral equation, which is important for the main findings, is proved. With the help of this integral equation that includes fractional integral operators with Mittag-Leffler kernel, many HH-type integral inequalities are derived for the functions whose absolute values of the second derivatives are s-convex and s-concave. Some classical inequalities and hypothesis conditions, such as Hölder’s inequality and Young’s inequality, are taken into account in the proof of the findings.

scholarly journals Certain Chebyshev Type Integral Inequalities Involving Hadamard’s Fractional Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Sotiris K. Ntouyas ◽  
Sunil D. Purohit ◽  
Jessada Tariboon
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Weighted Version ◽  
Fractional Integral Operators ◽  
Differentiable Functions ◽  
Type Integral ◽  
Chebyshev Functional

We establish certain new fractional integral inequalities for the differentiable functions whose derivatives belong to the spaceLp([1,∞)), related to the weighted version of the Chebyshev functional, involving Hadamard’s fractional integral operators. As an application, particular results have been also established.

scholarly journals Hermite–Jensen–Mercer-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Convex Function

2021 ◽  
Vol 5 (4) ◽  
pp. 269
Author(s):  
Miguel Vivas-Cortez ◽  
Muhammad Shoaib Saleem ◽  
Sana Sajid ◽  
Muhammad Sajid Zahoor ◽  
Artion Kashuri
Keyword(s):  
Convex Function ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Differentiable Mapping ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Fractional Differential ◽  
Integral Identities

Integral inequalities involving many fractional integral operators are used to solve various fractional differential equations. In the present paper, we will generalize the Hermite–Jensen–Mercer-type inequalities for an h-convex function via a Caputo–Fabrizio fractional integral. We develop some novel Caputo–Fabrizio fractional integral inequalities. We also present Caputo–Fabrizio fractional integral identities for differentiable mapping, and these will be used to give estimates for some fractional Hermite–Jensen–Mercer-type inequalities. Some familiar results are recaptured as special cases of our results.

scholarly journals On generalization of Fejér type inequalities via fractional integral operators

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5537-5547 ◽  
Author(s):  
Erhan Set ◽  
Ahmet Akdemir ◽  
Barış Çelik
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Differentiable Mapping ◽  
Fractional Integral Operators

In this paper we first prove a new lemma for differentiable mapping via a fractional integral operator. Then, using lemma, we establish some new Hermite-Hadamard-Fejer type results for convex functions via fractional integral operators. The results presented here would provide extensions of those given in earlier works.

scholarly journals On integral inequalities related to the weighted and the extended Chebyshev functionals involving different fractional operators

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Barış Çelik ◽  
Mustafa Ç. Gürbüz ◽  
M. Emin Özdemir ◽  
Erhan Set
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Fractional Integral Operators

AbstractThe role of fractional integral operators can be found as one of the best ways to generalize classical inequalities. In this paper, we use different fractional integral operators to produce some inequalities for the weighted and the extended Chebyshev functionals. The results are more general than the available classical results in the literature.

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