scholarly journals Some generalization of integral inequalities for twice differentiable mappings involving fractional integrals

2015 ◽  
Vol 7 (2) ◽  
pp. 251-264
Author(s):  
Mehmet Zeki Sarikaya ◽  
Huseyin Budak
Keyword(s):  
Integral Identity ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
General Integral ◽  
Differentiable Mappings

Abstract In this paper, a general integral identity involving Riemann- Liouville fractional integrals is derived. By use this identity, we establish new some generalized inequalities of the Hermite-Hadamard’s type for functions whose absolute values of derivatives are convex.

Some new generalizations for GA-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
Ahmet Akdemir ◽  
Özdemir Emin ◽  
Ardıç Avcı ◽  
Abdullatif Yalçın
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
General Integral ◽  
Second Derivatives ◽  
Derivatives Of

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

Some new fractional integral inequalities for generalized relative semi-m-(r; h1, h2)-preinvex mappings via generalized Mittag-Leffler function

2019 ◽  
Vol 26 (1/2) ◽  
pp. 41-55 ◽  
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Invex Set ◽  
Special Means ◽  
Special Cases ◽  
Differentiable Mappings

The authors discover a new identity concerning differentiable mappings defined on m-invex set via fractional integrals. By using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized relative semi- m-(r;h1,h2)-preinvex mappings by involving generalized Mittag-Leffler function are presented. It is pointed out that some new special cases can be deduced from main results of the paper. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.

scholarly journals On Some Integral Inequalities via Conformable Fractional Integrals

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ahmet Ocak Akdemir ◽  
Erhan Deniz ◽  
Ebru Yüksel
Keyword(s):  
Integral Identity ◽  
Present Note ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Special Cases ◽  
New Inequalities

AbstractIn the present note, we have given a new integral identity via Conformable fractional integrals and some further properties. We have proved some integral inequalities for different kinds of convexity via Conformable fractional integrals. We have also showed that special cases of our findings gave some new inequalities involving Riemann-Liouville fractional integrals.

Vectorial fractional integral inequalities with convexity

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
George Anastassiou
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
General Integral ◽  
Hardy Type ◽  
Wide Range ◽  
Left And Right ◽  
Multiple Integrals ◽  
P Type ◽  
Derivatives Of ◽  
Increasing Functions

AbstractHere we present vectorial general integral inequalities involving products of multivariate convex and increasing functions applied to vectors of functions. As specific applications we derive a wide range of vectorial fractional inequalities of Hardy type. These involve the left and right: Erdélyi-Kober fractional integrals, mixed Riemann-Liouville fractional multiple integrals. Next we produce multivariate Poincaré type vectorial fractional inequalities involving left fractional radial derivatives of Canavati type, Riemann-Liouville and Caputo types. The exposed inequalities are of L p type, p ≥ 1, and exponential type.

scholarly journals Fractional integral identity, estimation of its bounds and some applications to trapezoidal quadrature rule

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2629-2641
Author(s):  
Artion Kashuri ◽  
Muhammad Awan ◽  
Muhammad Noor
Keyword(s):  
Applied Sciences ◽  
Integral Identity ◽  
Fractional Integral ◽  
Quadrature Rule ◽  
The Other ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Trapezium Type ◽  
Type Integral ◽  
Preinvex Functions

The aim of this paper is to introduce a new extension of preinvexity called exponentially (m,?1,?2, h1,h2)-preinvexity. Some new integral inequalities of Hermite-Hadamard type for exponentially (m,?1,?2,h1,h2)-preinvex functions via Riemann-Liouville fractional integral are established. Also, some new estimates with respect to trapezium-type integral inequalities for exponentially (m,?1,?2,h1,h2)-preinvex functions via general fractional integrals are obtained. We show that the class of exponentially (m,?1,?2, h1,h2)-preinvex functions includes several other classes of preinvex functions. We shown by two basic examples the efficiency of the obtained inequalities on the base of comparing those with the other corresponding existing ones. At the end, some new error estimates for trapezoidal quadrature formula are provided as well. This results may stimulate further research in different areas of pure and applied sciences.

scholarly journals New General Integral Inequalities for Lipschitzian Functions via Hadamard Fractional Integrals

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
İmdat İşcan
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Positive Real ◽  
General Integral ◽  
Lipschitzian Functions ◽  
Special Means ◽  
Hadamard Fractional Integrals

The author obtains new estimates on generalization of Hadamard, Ostrowski, and Simpson type inequalities for Lipschitzian functions via Hadamard fractional integrals. Some applications to special means of positive real numbers are also given.

scholarly journals Generalization of Hermite-Hadamard inequalities involving Hadamard fractional integrals

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1515-1524 ◽  
Author(s):  
Zhi Zhang ◽  
Wei Wei ◽  
Jin Wang
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Fractional Integrals ◽  
Differentiable Mapping ◽  
Real Numbers ◽  
General Integral ◽  
Power Means ◽  
Special Means ◽  
Hadamard Fractional Integrals

In this paper, we firstly give a general integral identity for once differentiable mapping involving Hadamard fractional integrals. Secondly, we use this integral identity to derive some new generalization of fractional Hermite-Hadamard inequalities through GA-convex functions via power means and integrals GG-convex functions via power means. Some applications to special means of real numbers are given.

scholarly journals A new generalization of some quantum integral inequalities for quantum differentiable convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yi-Xia Li ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Quantum Integral ◽  
Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

scholarly journals Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

2021 ◽  
Vol 5 (3) ◽  
pp. 80
Author(s):  
Hari Mohan Srivastava ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Dumitru Baleanu ◽  
Y. S. Hamed
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Wright Function ◽  
Nonconvex Functions ◽  
Special Cases ◽  
Type Integral ◽  
Generic Class ◽  
Two Parameters ◽  
Class Of Functions

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

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