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7 results on '"Finite difference inequalities"'

1. Some new generalized Volterra–Fredholm type finite difference inequalities involving four iterated sums

Author

Feng, Qinghua, Meng, Fanwei, and Fu, Bosheng

Subjects
*VOLTERRA equations, *GENERALIZATION, *FREDHOLM equations, *FINITE differences, *MATHEMATICAL inequalities, *MATHEMATICAL bounds, *DIFFERENCE equations, *ITERATIVE methods (Mathematics)
Abstract

Abstract: In this paper, based on some new generalized Volterra–Fredholm type finite difference inequalities involving four iterated sums, we derive some new explicit bounds for the unknown functions concerned. These inequalities are of more general forms than some existing results in the literature, and are generalization of the main results of Ma [J. Comput. Appl. Math. 233 (2010) 2170–2180]. As application of the established results, we present a Volterra–Fredholm sum-difference equation, and research the qualitative as well as quantitative properties for it. [Copyright &y& Elsevier]

Published
2013
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2. New Estimates on Certain Fundamental Finite Difference Inequalities.

Author

Pachpatte, B. G.

Subjects
*FINITE differences, *MATHEMATICAL inequalities, *DIFFERENCE equations, *NUMERICAL analysis, *LIPSCHITZ spaces
Abstract

In the present note we establish new estimates on some fundamental finite difference inequalities which can be used as effective tools in the study of a class of sum-difference equations. Some applications are also given to convey the importance of one of our result. [ABSTRACT FROM AUTHOR]

Published
2009

3. Some new finite difference inequalities arising in the theory of difference equations

Author

Meng Fanwei, Feng Qinghua, and Zhang Yaoming

Subjects
Finite difference inequalities, Difference equations, Explicit bounds, Qualitative analysis, Quantitative analysis, Mathematics, QA1-939
Abstract

Abstract In this work, some new finite difference inequalities in two independent variables are established, which can be used in the study of qualitative as well as quantitative properties of solutions of certain difference equations. The established results extend some existing results in the literature. MSC 2010: 26D15

Published
2011

5. Some new finite difference inequalities

Author

B.G. Pachpatte

Subjects
Inequality, Differential equation, media_common.quotation_subject, Mathematical analysis, Finite difference method, Finite difference, Computational Mathematics, Bounds on the solutions, Computational Theory and Mathematics, Finite difference inequalities, Modeling and Simulation, Modelling and Simulation, Applied mathematics, Integral inequality, Finite difference and sum-difference equations, media_common, Mathematics
Abstract

In this paper, we establish some new finite difference inequalities related to a certain integral inequality arising in the theory of differential equations. The inequalities obtained here can be used as handy tools in the theory of some new classes of finite difference and sum-difference equations.

Published
1994
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6. On Some Finite Difference Inequalities in Two Independent Variables

Author

B.G. Pachpatte

Subjects
Variables, Inequality, finite difference and sum-difference equations, Applied Mathematics, media_common.quotation_subject, Finite difference method, Finite difference, sums and products, subadditive and submultiplicative functions, Calculus, Applied mathematics, nondecreasing, finite difference inequalities, two independent variables, nonincreasing, Analysis, Mathematics, media_common
Abstract

In this article, we establish some new finite difference inequalities in two independent variables which can be used as tools in the study of certain classes of finite difference and sum-difference equations.

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7. Some new finite difference inequalities arising in the theory of difference equations

Author

Yaoming Zhang, Qinghua Feng, and Fanwei Meng

Subjects
Difference equations, Algebra and Number Theory, Independent equation, lcsh:Mathematics, Applied Mathematics, Mathematical analysis, Numerical methods for ordinary differential equations, Finite difference method, Finite difference, Finite difference coefficient, Explicit bounds, Time-scale calculus, lcsh:QA1-939, Finite difference inequalities, Simultaneous equations, Quantitative analysis, Qualitative analysis, Analysis, Numerical partial differential equations, Mathematics
Abstract

In this work, some new finite difference inequalities in two independent variables are established, which can be used in the study of qualitative as well as quantitative properties of solutions of certain difference equations. The established results extend some existing results in the literature. MSC 2010: 26D15

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