Inequalities for Finite Difference Equations
"A treatise on finite difference ineuqalities that have important applications to theories of various classes of finite difference and sum-difference equations, including several linear and nonlinear finite difference inequalities appearing for the first time in book form."
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A'0 be chosen A^then application of Theorem applying Theorem AQ,then assume asymptotically stable bound completed as mentioned completed by following de1ined Define a function defined for x.y defined in Theorem defined on A'0 desired inequality difference inequalities easy to observe established by Pachpatte finite difference equations finite-difference inequalities following the proof for0 forx forx.y function z(t function z(x.y given by Pachpatte given in Theorem inequality established inequality given inTheorem inverse function keeping v fixed Let g(u Let the function Let u(t Let u(x.y nondecreasing function defined nonlinear finite-difference nonnegative and nondecreasing nonnegative constant nonnegative functions defined numerical analysis obtain the estimate omit the details Pachpatte 179 Pachpatte has established positive functions defined proof is complete proof of Theorem real-valued functions defined real-valued nonnegative functions required inequality right side satisfies the condition solution of Equation stability suitable application sum-difference equations tions x-l y-l yields