Abstract

The present research offers insight into the connections between higher-order difference equations with iterated sums and symmetric functions, as well as the resulting inequalities from these interactions. In this study, we introduce new difference inequalities of an algebraic nature that use symmetric functions to handle significant higher-order nonlinear finite difference equations with iterated sums. With the aid of these results, it will be simple to examine a collection of higher-order nonlinear finite difference equations with iterated sums. Finally, we study the boundedness, uniqueness, and continuous dependency of the solution on the initial data of a class of iterated difference equations. Furthermore, we present a numerical illustration to highlight the relevance of our findings.

Keywords and Phrases

Symmetric functions, Difference inequalities, Higher-order difference equations, Iterated sums.

A.M.S. subject classification

26D15, 26D07, 39A22, 39A13, 39B12.

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