Some New Results on Hermite–Hadamard–Mercer-Type Inequalities Using a General Family of Fractional Integral Operators

2021 ◽  
Vol 5 (3) ◽  
pp. 68
Author(s):  
Erhan Set ◽  
Barış Çelik ◽  
M. Emin Özdemir ◽  
Mücahit Aslan
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Absolute Value ◽  
General Family

The aim of this article is to obtain new Hermite–Hadamard–Mercer-type inequalities using Raina’s fractional integral operators. We present some distinct and novel fractional Hermite–Hadamard–Mercer-type inequalities for the functions whose absolute value of derivatives are convex. Our main findings are generalizations and extensions of some results that existed in the literature.

scholarly journals New Chebyshev type inequalities via a general family of fractional integral operators with a modified Mittag-Leffler kernel

2021 ◽  
Vol 6 (10) ◽  
pp. 11167-11186
Author(s):  
Hari M. Srivastava ◽  
◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Abdullah M. Alsharif ◽  
...  
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Chebyshev Inequality ◽  
Fractional Integral Operators ◽  
General Family ◽  
Chebyshev Functional ◽  
Bounded Below

<abstract><p>The main goal of this article is first to introduce a new generalization of the fractional integral operators with a certain modified Mittag-Leffler kernel and then investigate the Chebyshev inequality via this general family of fractional integral operators. We improve our results and we investigate the Chebyshev inequality for more than two functions. We also derive some inequalities of this type for functions whose derivatives are bounded above and bounded below. In addition, we establish an estimate for the Chebyshev functional by using the new fractional integral operators. Finally, we find similar inequalities for some specialized fractional integrals keeping some of the earlier results in view.</p></abstract>

scholarly journals Hermite-Hadamard Type Inequalities for convex functions via generalized fractional integral operators

2016 ◽  
Vol 5 (1) ◽  
pp. 55-62
Author(s):  
Erhan Set ◽  
Abdurrahman Gözpinar
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Absolute Value ◽  
Type Integral ◽  
Generalized Fractional Integral ◽  
Fractional Type ◽  
Generalized Fractional Integral Operators

AbstractIn this present work, the authors establish a new integral identity involving generalized fractional integral operators and by using this fractional-type integral identity, obtain some new Hermite-Hadamard type inequalities for functions whose first derivatives in absolute value are convex. Relevant connections of the results presented here with those earlier ones are also pointed out.

scholarly journals Some novel inequalities involving a function’s fractional integrals in relation to another function through generalized quasiconvex mappings

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3349-3360
Author(s):  
Eze Nwaeze ◽  
Artion Kashuri
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Fractional Integral Operators ◽  
Absolute Value ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators ◽  
New Inequalities

In this paper, we establish new inequalities of the Hermite-Hadamard, midpoint and trapezoid types for functions whose first derivatives in absolute value are ?-quasiconvex by means of generalized fractional integral operators with respect to another function ? : [?,?] ? (0,?). Our theorems reduce to results involving the Riemann-Liouville fractional integral operators if ? is the identity map, and results involving the Hadamard operators if ?(x) = ln x. More inequalities can be deduced by choosing different bifunctions for ?. To the best of our knowledge, the results obtained herein are new and we hope that they will stimulate further interest in this direction.

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.

scholarly journals Two-weight norm inequalities for fractional integral operators with $A_{\lambda,\infty}$ weights

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Junren Pan ◽  
Wenchang Sun
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Type Estimate ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
New Class ◽  
Formula Type

Abstract In this paper, we introduce a new class of weights, the $A_{\lambda, \infty}$Aλ,∞ weights, which contains the classical $A_{\infty}$A∞ weights. We prove a mixed $A_{p,q}$Ap,q–$A_{\lambda,\infty}$Aλ,∞ type estimate for fractional integral operators.

On Chebychev type inequalities for fractional integral operators

2017 ◽  
Author(s):  
Fuat Usta ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarıkaya
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators
Sign in / Sign up

Export Citation Format

Share Document