scholarly journals On a new Ostrowski type inequality in two independent variables

2001 ◽  
Vol 32 (1) ◽  
pp. 45-49
Author(s):  
B. G. Pachpatte
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Discrete Analogue ◽  
Independent Variables ◽  
Ostrowski Type Inequality ◽  
Two Independent Variables

In this note a new integral inequality of Ostrowski type in two independent variables is established. The discrete analogue of the main result is also given.

New generalized 2D Ostrowski type inequalities on time scales with k2 points using a parameter

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3155-3169 ◽  
Author(s):  
Seth Kermausuor ◽  
Eze Nwaeze
Keyword(s):  
Numerical Analysis ◽  
Time Scales ◽  
Type Inequality ◽  
Dimensional Case ◽  
Multiple Points ◽  
Quantum Calculus ◽  
Independent Variables ◽  
Ostrowski Type Inequality ◽  
Two Independent Variables

Recently, a new Ostrowski type inequality on time scales for k points was proved in [G. Xu, Z. B. Fang: A Generalization of Ostrowski type inequality on time scales with k points. Journal of Mathematical Inequalities (2017), 11(1):41-48]. In this article, we extend this result to the 2-dimensional case. Besides extension, our results also generalize the three main results of Meng and Feng in the paper [Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables. Journal of Inequalities and Applications (2012), 2012:74]. In addition, we apply some of our theorems to the continuous, discrete, and quantum calculus to obtain more interesting results in this direction. We hope that results obtained in this paper would find their place in approximation and numerical analysis.

scholarly journals On the Generalized Weighted Integral Inequality for Double Integrals

2015 ◽  
Vol 61 (1) ◽  
pp. 169-179 ◽  
Author(s):  
Mehmet Zeki Sarikaya
Keyword(s):  
Integral Inequality ◽  
Independent Variables ◽  
Elementary Analysis ◽  
Weighted Integral ◽  
Function Of Two Variables ◽  
Two Independent Variables ◽  
Double Integrals

Abstract In this paper, we obtain weighted Montgomery’s identities for function of two variables and apply them to give new generalization weighted integral inequality for double integrals involving functions of two independent variables by using fairly elementary analysis.

scholarly journals A NOTE ON TWO DIMENSIONAL INTEGRAL INEQUALITY

1990 ◽  
Vol 21 (3) ◽  
pp. 211-213
Author(s):  
B. G. PACHPATTE
Keyword(s):  
Integral Inequality ◽  
Present Note ◽  
Two Dimensional ◽  
Partial Derivatives ◽  
Independent Variables ◽  
Dimensional Integral ◽  
Two Independent Variables

In the present note we establish a new integral inequality involving a function of two independent variables and its partial derivatives.

scholarly journals A general Ostrowski type inequality for double integrals

2002 ◽  
Vol 33 (4) ◽  
pp. 319-334
Author(s):  
G. Hanna ◽  
S. S. Dragomir ◽  
P. Cerone
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Two Dimensions ◽  
One Dimensional ◽  
Ostrowski Type Inequality ◽  
And Function ◽  
Interior Points ◽  
Double Integrals ◽  
Differentiable Mappings

Some generalisations of an Ostrowski Type Inequality in two dimensions for $n-$time differentiable mappings are given. The result is an Integral Inequality with bounded $n-$time derivatives. This is employed to approximate double integrals using one dimensional integrals and function evaluations at the boundary and interior points.

A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation

2020 ◽  
Vol 21 (7-8) ◽  
pp. 667-673
Author(s):  
Mohammad Wajeeh Alomari
Keyword(s):  
Bounded Variation ◽  
Integral Inequality ◽  
Type Inequality ◽  
Quadrature Rule ◽  
Ostrowski Type Inequality

AbstractA weighted companion of Ostrowski type inequality is established. Some sharp inequalities are proved. Application to a quadrature rule is provided.

scholarly journals New Hermite-Hadamard type inequalities for m and (α, m)-convex functions on the coordinates via generalized fractional integrals

2021 ◽  
Vol 40 (6) ◽  
pp. 1449-1472
Author(s):  
Seth Kermausuor
Keyword(s):  
Convex Functions ◽  
Type Inequality ◽  
Second Order ◽  
Fractional Integrals ◽  
Absolute Value ◽  
Partial Derivatives ◽  
Independent Variables ◽  
Functions Of Two Variables ◽  
Derivatives Of ◽  
Two Independent Variables

In this paper, we obtained a new Hermite-Hadamard type inequality for functions of two independent variables that are m-convex on the coordinates via some generalized Katugampola type fractional integrals. We also established a new identity involving the second order mixed partial derivatives of functions of two independent variables via the generalized Katugampola fractional integrals. Using the identity, we established some new Hermite-Hadamard type inequalities for functions whose second order mixed partial derivatives in absolute value at some powers are (α, m)-convex on the coordinates. Our results are extensions of some earlier results in the literature for functions of two variables.

scholarly journals On the Ostrowski type integral inequality for double integrals

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
Mehmet Zeki Sarikaya
Keyword(s):  
Integral Inequality ◽  
Independent Variables ◽  
Elementary Analysis ◽  
Type Integral ◽  
Two Independent Variables ◽  
Double Integrals

AbstractIn this note, we establish a new inequality of Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.

scholarly journals OPIAL TYPE INEQUALITY IN SEVERAL VARIABLES

1991 ◽  
Vol 22 (1) ◽  
pp. 7-11
Author(s):  
B. G. PACHPATTE
Keyword(s):  
Partial Derivative ◽  
Integral Inequality ◽  
Present Note ◽  
Type Inequality ◽  
Discrete Analogue ◽  
Several Variables

In the present note we establish a new integral inequality of the Opial type mvolving a function of $n$ variables and its partial derivative. A corresponding result on the discrete analogue of the main result is also given.

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