scholarly journals New Hermite Hadamard type inequalities for twice differentiable convex mappings via Green function and applications

2016 ◽  
Vol 2 (2) ◽  
pp. 107-118 ◽  
Author(s):  
Samet Erden ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Green Function ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Absolute Value ◽  
Convex Mappings ◽  
Trapezoidal Formula ◽  
Special Means ◽  
Second Derivatives ◽  
Type Integral

Abstract We derive some Hermite Hamamard type integral inequalities for functions whose second derivatives absolute value are convex. Some eror estimates for the trapezoidal formula are obtained. Finally, some natural applications to special means of real numbers are given

scholarly journals New inequalities of Hermite-Hadamard type for n-times differentiable convex and concave functions with applications

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2609-2621
Author(s):  
M.A. Latif ◽  
S.S. Dragomir
Keyword(s):  
Concave Functions ◽  
Absolute Value ◽  
Trapezoidal Formula ◽  
Special Means ◽  
Second Derivatives ◽  
Special Cases ◽  
New Inequalities

In this paper, a new identity for n-times differntiable functions is established and by using the obtained identity, some new inequalities Hermite-Hadamard type are obtained for functions whose nth derivatives in absolute value are convex and concave functions. From our results, several inequalities of Hermite-Hadamard type can be derived in terms of functions whose first and second derivatives in absolute value are convex and concave functions as special cases. Our results may provide refinements of some results already exist in literature. Applications to trapezoidal formula and special means of established results 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 Some integral inequalities for multiplicatively geometrically P-functions

2019 ◽  
Vol 9 (2) ◽  
pp. 216-222 ◽  
Author(s):  
Huriye Kadakal
Keyword(s):  
Integral Inequalities ◽  
Real Numbers ◽  
Absolute Value ◽  
General Identity ◽  
Differentiable Functions ◽  
Special Means

In this manuscript, by using a general identity for differentiable functions we can obtain new estimates on a generalization of Hadamard, Ostrowski and Simpson type inequalities for functions whose derivatives in absolute value at certain power are multiplicatively geometrically P-functions. Some applications to special means of real numbers are also given.

scholarly journals Fractional Integral Inequalities for Differentiable Convex Mappings and Applications to Special Means and a Midpoint Formula

2012 ◽  
Vol 8 (2) ◽  
pp. 21-28 ◽  
Author(s):  
Chun Zhu ◽  
Michal Fečkan ◽  
Jinrong Wang
Keyword(s):  
Error Estimates ◽  
Integral Identity ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Liouville Type ◽  
Convex Mappings ◽  
Special Means

Abstract In this paper, Riemann-Liouville type fractional integral identity and inequality for differentiable convex mappings are studied. Some applications to special means of real numbers are given. Finally, error estimates for a midpoint formula are also obtained.

Some weighted integral inequalities for differentiable h-preinvex functions

2018 ◽  
Vol 25 (3) ◽  
pp. 441-450 ◽  
Author(s):  
Muhammad Amer Latif ◽  
Sever Silvestru Dragomir ◽  
Ebrahim Momoniat
Keyword(s):  
Integral Inequality ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Absolute Value ◽  
Type Integral ◽  
Weighted Integral ◽  
Preinvex Functions ◽  
Special Case

AbstractIn this paper, by using a weighted identity for functions defined on an open invex subset of the set of real numbers, by using the Hölder integral inequality and by using the notion of h-preinvexity, we present weighted integral inequalities of Hermite–Hadamard-type for functions whose derivatives in absolute value raised to certain powers are h-preinvex functions. Some new Hermite–Hadamard-type integral inequalities are obtained when h is super-additive. Inequalities of Hermite–Hadamard-type for s-preinvex functions are given as well as a special case of our results.

scholarly journals New fractional inequalities of midpoint type via s-convexity and their application

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ohud Almutairi ◽  
Adem Kılıçman
Keyword(s):  
Error Estimates ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Special Means ◽  
Second Derivatives ◽  
The Absolute ◽  
New Inequalities

Abstract In this study, we introduced new integral inequalities of Hermite–Hadamard type via s-convexity and studied their properties. The absolute form of the first and second derivatives for the new inequalities is considered to be s-convex. As an application, the inequalities were applied to the special means of real numbers. We give the error estimates for the midpoint formula.

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 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.

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