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 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 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 Growth estimates on certain integral inequalities in two variables involving iterated integrals

2005 ◽  
Vol 36 (3) ◽  
pp. 179-191
Author(s):  
B. G. Pachpatte
Keyword(s):  
Integral Equations ◽  
Integral Inequalities ◽  
Qualitative Behavior ◽  
Iterated Integrals ◽  
Independent Variables ◽  
Two Independent Variables ◽  
Double Integrals

The aim of the present paper is to establish growth estimates on some new integral inequalities in two independent variables involving iterated double integrals, which can be used to study the qualitative behavior of solutions of certain partial integrodifferential and integral equations. Applications are also given to illustrate the usefulness of one of our results.

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.

scholarly journals Some properties of approximants for branched continued fractions of the special form with positive and alternating-sign partial numerators

2018 ◽  
Vol 10 (1) ◽  
pp. 3-13 ◽  
Author(s):  
T.M. Antonova ◽  
M.V. Dmytryshyn ◽  
S.M. Vozna
Keyword(s):  
Continued Fractions ◽  
Special Form ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Rational Approximants ◽  
Independent Variables ◽  
Function Of Two Variables ◽  
Necessary And Sufficient ◽  
Double Power Series ◽  
Two Independent Variables

The paper deals with research of convergence for one of the generalizations of continued fractions -- branched continued fractions of the special form with two branches. Such branched continued fractions, similarly as the two-dimensional continued fractions and the branched continued fractions with two independent variables are connected with the problem of  the correspondence between a formal double power series and a sequence of the rational approximants of a function of two variables. Unlike continued fractions, approximants of which are constructed unambiguously, there are many ways to construct approximants of branched continued fractions of the general and the special form. The paper examines the ordinary approximants and one of the structures of figured approximants of the studied branched continued fractions, which is connected with the problem of correspondence. We consider some properties of approximants of such fractions, whose partial numerators are positive and alternating-sign  and partial denominators are equal to one. Some necessary and sufficient conditions for figured convergence are established. It is proved that under these conditions from the convergence of the sequence of figured approximants it follows the convergence of the sequence of ordinary approximants  to the same limit.

scholarly journals The Numerical Evaluation of Double Integrals

1923 ◽  
Vol 42 ◽  
pp. 2-13 ◽  
Author(s):  
A. C. Aitken ◽  
G. L. Frewin
Keyword(s):  
Numerical Evaluation ◽  
Systematic Search ◽  
Independent Variables ◽  
Two Independent Variables ◽  
Double Integrals

The present paper is concerned with formulae by which double integrals of functions of two independent variables may be evaluated approximately. The number of such formulae published hitherto is not great, and it has seemed desirable both to make a systematic search for new formulae, and to test the comparative merits of these, and of those previously known, by computing the numerical values of certain selected integrals.

scholarly journals Nonlinear integral inequality in two independent variables

1988 ◽  
Vol 11 (1) ◽  
pp. 115-119
Author(s):  
P. T. Vaz ◽  
S. G. Deo
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Integral Inequality ◽  
Nonlinear Partial Differential Equation ◽  
Partial Differential ◽  
Independent Variables ◽  
Nonlinear Integral Inequality ◽  
Nonlinear Inequality ◽  
Two Independent Variables

In this note, the authors obtain a generalization of the integral inequality of Bihari [1] to a nonlinear inequality in two independent variables. With the aid of this inequality a bound for the solution of a nonlinear partial differential equation is established.

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.

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