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.

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 Some new generalized $ \kappa $–fractional Hermite–Hadamard–Mercer type integral inequalities and their applications

2021 ◽  
Vol 7 (2) ◽  
pp. 3203-3220
Author(s):  
Miguel Vivas-Cortez ◽  
◽  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Artion Kashuri ◽  
...  
Keyword(s):  
Quadrature Formula ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Error Estimations ◽  
Integral Identities

<abstract><p>In this paper, we have established some new Hermite–Hadamard–Mercer type of inequalities by using $ {\kappa} $–Riemann–Liouville fractional integrals. Moreover, we have derived two new integral identities as auxiliary results. From the applied identities as auxiliary results, we have obtained some new variants of Hermite–Hadamard–Mercer type via $ {\kappa} $–Riemann–Liouville fractional integrals. Several special cases are deduced in detail and some know results are recaptured as well. In order to illustrate the efficiency of our main results, some applications regarding special means of positive real numbers and error estimations for the trapezoidal quadrature formula are provided as well.</p></abstract>

scholarly journals Some new bounds оf Gauss – Jacobi аnd Hermite – Hadamard type integral inequalities

2021 ◽  
Vol 73 (8) ◽  
pp. 1067-1084
Author(s):  
A. Kashuri ◽  
M. Ramosaçaj ◽  
R. Liko
Keyword(s):  
Error Estimates ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Special Cases ◽  
Type Integral

UDC 517.5 In this paper, authors discover two interesting identities regarding Gauss–Jacobi and Hermite–Hadamard type integral inequalities. By using the first lemma as an auxiliary result, some new bounds with respect to Gauss–Jacobi type integral inequalities are established. Also, using the second lemma, some new estimates with respect to Hermite–Hadamard type integral inequalities via general fractional integrals are obtained. It is pointed out that some new special cases can be deduced from main results. Some applications to special means for different positive real numbers and new error estimates for the trapezoidal are provided as well. These results give us the generalizations, refinement and significant improvements of the new and previous known results. The ideas and techniques of this paper may stimulate further research.

scholarly journals Fractional integral inequalities for generalized-$$\mathbf{m }$$-$$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$-convex mappings via an extended generalized Mittag–Leffler function

2019 ◽  
Vol 9 (2) ◽  
pp. 231-243
Author(s):  
George Anastassiou ◽  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Convex Mappings ◽  
Invex Set ◽  
Special Means ◽  
Special Cases

AbstractThe authors discover a new identity concerning differentiable mappings defined on $$\mathbf{m }$$ m -invex set via general fractional integrals. Using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized-$$\mathbf{m }$$ m -$$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings by involving an extended generalized Mittag–Leffler function are presented. It is pointed out that some new special cases can be deduced from main results. 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 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 Fejér type integral inequalities related with geometrically-arithmetically convex functions with applications

2019 ◽  
Vol 23 (1) ◽  
pp. 51-64
Author(s):  
S. S. Dragomir ◽  
M. A. Latif ◽  
E. Momoniat
Keyword(s):  
Differentiable Function ◽  
Integral Inequality ◽  
Convex Functions ◽  
Symmetric Function ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Left Part ◽  
Special Means ◽  
Type Integral

A new identity involving a geometrically symmetric function and a differentiable function is established. Some new Fejér type integral inequalities, connected with the left part of Hermite–Hadamard type inequalities for geometrically-arithmetically convex functions, are presented by using the Hölder integral inequality and the notion of geometrically-arithmetically convexity. Applications of our results to special means of positive real numbers are given.

scholarly journals Some Fejér type integral inequalities for geometrically-arithmetically-convex functions with applications

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2193-2206 ◽  
Author(s):  
Muhammad Latif ◽  
Sever Dragomir ◽  
Ebrahim Momoniat
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Symmetric Functions ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Type Integral

In this paper, the notion of geometrically symmetric functions is introduced. A new identity involving geometrically symmetric functions is established, and by using the obtained identity, the H?lder integral inequality and the notion of geometrically-arithmetically convexity, some new Fej?r type integral inequalities are presented. Applications of our results to special means of positive real numbers are given as well.

scholarly journals On Some New Hermite-Hadamard Type Inequalities fors-Geometrically Convex Functions

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

Some new integral inequalities of Hermite-Hadamard type related to thes-geometrically convex functions are established and some applications to special means of positive real numbers are also given.

scholarly journals New Simpson Type Integral Inequalities for s -Convex Functions and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Faraidun Hamasalh ◽  
Yuming Chu
Keyword(s):  
Error Estimation ◽  
Convex Functions ◽  
Bessel Functions ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Theoretical Results

First, we consider a new Simpson’s identity. This identity investigates our main results that consist of some integral inequalities of Simpson’s type for the s –convex functions. From our main results, we obtain some special cases which are discussed in detail. Finally, some applications on the Bessel functions, special means of distinct positive real numbers, and error estimation about Simpson quadrature formula are presented to support our theoretical results.

scholarly journals New Inequalities of Fejer´ and Hermite-Hadamard type Concerning Convex and QuasiConvex Functions With Applications

2021 ◽  
pp. 83-99
Author(s):  
Muhammad Amer Latif ◽  
Sever Silvestru Dragomir ◽  
Sofian Obeidat
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Quasiconvex Functions ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
New Inequalities

This research contains new integral inequalities of Fejer and ´ Hermite-Hadamard type involving convex and quasi-convex functions. Applications of the newly established results for special means of positive real numbers are given.

Sign in / Sign up

Export Citation Format

Share Document