scholarly journals Fractional Hermite–Hadamard–Fejer Inequalities for a Convex Function with Respect to an Increasing Function Involving a Positive Weighted Symmetric Function

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1503 ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Artion Kashuri
Keyword(s):  
Fractional Calculus ◽  
Convex Function ◽  
Symmetric Function ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Fractional Operators ◽  
Important Direction ◽  
Increasing Function

There have been many different definitions of fractional calculus presented in the literature, especially in recent years. These definitions can be classified into groups with similar properties. An important direction of research has involved proving inequalities for fractional integrals of particular types of functions, such as Hermite–Hadamard–Fejer (HHF) inequalities and related results. Here we consider some HHF fractional integral inequalities and related results for a class of fractional operators (namely, the weighted fractional operators), which apply to function of convex type with respect to an increasing function involving a positive weighted symmetric function. We can conclude that all derived inequalities in our study generalize numerous well-known inequalities involving both classical and Riemann–Liouville fractional integral inequalities.

scholarly journals Hermite-Hadamard-Fejér type fractional inequalities relating to a convex harmonic function and a positive symmetric increasing function

2021 ◽  
Vol 7 (3) ◽  
pp. 4176-4198
Author(s):  
Muhammad Amer Latif ◽  
◽  
Humaira Kalsoom ◽  
Zareen A. Khan ◽  
◽  
...  
Keyword(s):  
Harmonic Function ◽  
Convex Functions ◽  
Symmetric Function ◽  
Fractional Integral ◽  
Harmonic Mean ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Harmonic Convex ◽  
Increasing Function

<abstract><p>The purpose of this article is to discuss some midpoint type HHF fractional integral inequalities and related results for a class of fractional operators (weighted fractional operators) that refer to harmonic convex functions with respect to an increasing function that contains a positive weighted symmetric function with respect to the harmonic mean of the endpoints of the interval. It can be concluded from all derived inequalities that our study generalizes a large number of well-known inequalities involving both classical and Riemann-Liouville fractional integral inequalities.</p></abstract>

scholarly journals On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity

2022 ◽  
Vol 6 (1) ◽  
pp. 28
Author(s):  
Tao Yan ◽  
Ghulam Farid ◽  
Hafsa Yasmeen ◽  
Chahn Yong Jung
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Generalized Convexity ◽  
Monotone Function ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Hadamard Inequality

In the literature of mathematical inequalities, convex functions of different kinds are used for the extension of classical Hadamard inequality. Fractional integral versions of the Hadamard inequality are also studied extensively by applying Riemann–Liouville fractional integrals. In this article, we define (α,h−m)-convex function with respect to a strictly monotone function that unifies several types of convexities defined in recent past. We establish fractional integral inequalities for this generalized convexity via Riemann–Liouville fractional integrals. The outcomes of this work contain compact formulas for fractional integral inequalities which generate results for different kinds of convex functions.

scholarly journals General Raina fractional integral inequalities on coordinates of convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Badreddine Meftah
Keyword(s):  
Mathematical Model ◽  
Fractional Calculus ◽  
Convex Function ◽  
Mathematical Analysis ◽  
Integral Inequality ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Differentiable Functions ◽  
Special Cases

AbstractIntegral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In this study, authors have established some generalized Raina fractional integral inequalities using an $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates. Also, we obtain an integral identity for partial differentiable functions. As an effect of this result, two interesting integral inequalities for the $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates are given. Finally, we can say that our findings recapture some recent results as special cases.

scholarly journals Generalized fractional integral inequalities of Hermite-Hadamard-type for a convex function

2020 ◽  
Vol 18 (1) ◽  
pp. 794-806 ◽  
Author(s):  
Jiangfeng Han ◽  
Pshtiwan Othman Mohammed ◽  
Huidan Zeng
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Primary Objective ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Generalized Fractional Integral

Abstract The primary objective of this research is to establish the generalized fractional integral inequalities of Hermite-Hadamard-type for MT-convex functions and to explore some new Hermite-Hadamard-type inequalities in a form of Riemann-Liouville fractional integrals as well as classical integrals. It is worth mentioning that our work generalizes and extends the results appeared in the literature.

scholarly journals Hadamard and Fejér–Hadamard Inequalities for α , h − m − p -Convex Functions via Riemann–Liouville Fractional Integrals

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Wenyan Jia ◽  
Muhammad Yussouf ◽  
Ghulam Farid ◽  
Khuram Ali Khan
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Different Types ◽  
Hadamard Fractional Integral

In this paper, we introduce α , h − m − p -convex function and some related functions. By applying this generalized definition, new versions of Hadamard and Fejér–Hadamard fractional integral inequalities for Riemann–Liouville fractional integrals are given. The presented results hold at the same time for different types of convexities.

scholarly journals Fractional Hermite–Jensen–Mercer Integral Inequalities with respect to Another Function and Application

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-30
Author(s):  
Saad Ihsan Butt ◽  
Muhammad Umar ◽  
Khuram Ali Khan ◽  
Artion Kashuri ◽  
Homan Emadifar
Keyword(s):  
Convex Function ◽  
Bessel Function ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Modified Bessel Function ◽  
Special Cases

In this paper, authors prove new variants of Hermite–Jensen–Mercer type inequalities using ψ –Riemann–Liouville fractional integrals with respect to another function via convexity. We establish generalized identities involving ψ –Riemann–Liouville fractional integral pertaining first and twice differentiable convex function λ , and these will be used to derive novel estimates for some fractional Hermite–Jensen–Mercer type inequalities. Some known results are recaptured from our results as special cases. Finally, an application from our results using the modified Bessel function of the first kind is established as well.

scholarly journals Inequalities for a Unified Integral Operator for Strongly α , m -Convex Function and Related Results in Fractional Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Chahn Yong Jung ◽  
Ghulam Farid ◽  
Kahkashan Mahreen ◽  
Soo Hak Shim
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Special Cases ◽  
Definition Of

In this paper, we study integral inequalities which will provide refinements of bounds of unified integral operators established for convex and α , m -convex functions. A new definition of function, namely, strongly α , m -convex function is applied in different forms and an extended Mittag-Leffler function is utilized to get the required results. Moreover, the obtained results in special cases give refinements of fractional integral inequalities published in this decade.

scholarly journals On Some Fractional Integral Inequalities of Hermite-Hadamard’s Type through Convexity

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 137 ◽  
Author(s):  
Shahid Qaisar ◽  
Jamshed Nasir ◽  
Saad Butt ◽  
Sabir Hussain
Keyword(s):  
Convex Function ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals

In this paper, we incorporate the notion of convex function and establish new integral inequalities of type Hermite–Hadamard via Riemann—Liouville fractional integrals. It is worth mentioning that the obtained inequalities generalize Hermite–Hadamard type inequalities presented by Özdemir, M.E. et. al. (2013) and Sarikaya, M.Z. et. al. (2011).

scholarly journals Refinements of some fractional integral inequalities for refined $(\alpha ,h-m)$-convex function

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Chahn Yong Jung ◽  
Ghulam Farid ◽  
Hafsa Yasmeen ◽  
Yu-Pei Lv ◽  
Josip Pečarić
Keyword(s):  
Convex Function ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
New Inequalities

AbstractThis article investigates new inequalities for generalized Riemann–Liouville fractional integrals via the refined $(\alpha ,h-m)$ ( α , h − m ) -convex function. The established results give refinements of fractional integral inequalities for $(h-m)$ ( h − m ) -convex, $(\alpha ,m)$ ( α , m ) -convex, $(s,m)$ ( s , m ) -convex, and related functions. Also, the k-fractional versions of given inequalities by using a parameter substitution are provided.

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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