scholarly journals Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications

2016 ◽  
Vol 2 (1) ◽  
pp. 12-32 ◽  
Author(s):  
M. A. Latif ◽  
S. S. Dragomir ◽  
E. Momoniat
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Random Variables ◽  
Integral Inequalities ◽  
Weighted Integral ◽  
Weighted Quadrature

Abstract In this paper, a new weighted identity for functions defined on a rectangle from the plane is established. By using the obtained identity and analysis, some new weighted integral inequalities for the classes of co-ordinated convex, co-ordinated wright-convex and co-ordinated quasi-convex functions on the rectangle from the plane are established which provide weighted generalization of some recent results proved for co-ordinated convex functions. Some applications of our results to random variables and 2D weighted quadrature formula are given as well.

scholarly journals On some weighted integral inequalities for convex functions related to Fejér’s result

Filomat ◽  
2011 ◽  
Vol 25 (1) ◽  
pp. 195-218
Author(s):  
K.L. Tseng ◽  
Shiow-Ru Hwang ◽  
S.S. Dragomir
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Integral Means ◽  
Weighted Integral

In this paper, we introduce some functionals associated with weighted integral means for convex functions. Some new Fej?r-type inequalities are obtained as well.

scholarly journals On Weighted Simpson’s 38 Rule

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1933
Author(s):  
Mohsen Rostamian Delavar ◽  
Artion Kashuri ◽  
Manuel De La De La Sen
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Type Inequality ◽  
Random Variables ◽  
Numerical Approximations ◽  
Weighted Version ◽  
Definite Integrals ◽  
Special Means ◽  
Error Estimations ◽  
Moments Of Random Variables

Numerical approximations of definite integrals and related error estimations can be made using Simpson’s rules (inequalities). There are two well-known rules: Simpson’s 13 rule or Simpson’s quadrature formula and Simpson’s 38 rule or Simpson’s second formula. The aim of the present paper is to extend several inequalities that hold for Simpson’s 13 rule to Simpson’s 38 rule. More precisely, we prove a weighted version of Simpson’s second type inequality and some Simpson’s second type inequalities for Lipschitzian, bounded variations, convex functions and the functions that belong to Lq. Some applications of the second type Simpson’s inequalities relate to approximations of special means and Simpson’s 38 formula, and moments of random variables are made.

scholarly journals On some weighted integral inequalities for convex functions related to Fejér's result

Filomat ◽  
2010 ◽  
Vol 24 (3) ◽  
pp. 125-148 ◽  
Author(s):  
K.L. Tseng ◽  
Shiow-Ru Hwang ◽  
S.S. Dragomir
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Integral Means ◽  
Weighted Integral

In this paper, we introduce some functionals associated with weighted integral means for convex functions. Some new Fej?r-type inequalities are obtained as well.

scholarly journals The Ostrowski inequality for $ s $-convex functions in the third sense

2022 ◽  
Vol 7 (4) ◽  
pp. 5605-5615
Author(s):  
Gültekin Tınaztepe ◽  
◽  
Sevda Sezer ◽  
Zeynep Eken ◽  
Sinem Sezer Evcan ◽  
...  
Keyword(s):  
Error Estimate ◽  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Power Mean ◽  
Ostrowski Inequality ◽  
Riemann Sums ◽  
The Third ◽  
The Absolute

<abstract><p>In this paper, the Ostrowski inequality for $ s $-convex functions in the third sense is studied. By applying Hölder and power mean integral inequalities, the Ostrowski inequality is obtained for the functions, the absolute values of the powers of whose derivatives are $ s $-convex in the third sense. In addition, by means of these inequalities, an error estimate for a quadrature formula via Riemann sums and some relations involving means are given as applications.</p></abstract>

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.

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 Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in ℝn\mathbb{R}^{n}

2020 ◽  
Vol 26 (1) ◽  
pp. 67-77 ◽  
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Euclidean Space ◽  
Convex Functions ◽  
Convex Bodies ◽  
Integral Inequalities ◽  
Divergence Theorem ◽  
Several Variables ◽  
Type Integral ◽  
Bounded Convex

AbstractIn this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space {\mathbb{R}^{n}} for any {n\geq 2}.

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