# Stability And Boundedness In Nonlinear And Neutral Difference Equations using New Variation of Parameters Formula And Fixed Point Theory

### Abstract

In the case of nonlinear problems, whether in differential or difference equations, it is difficult and in some cases impossible to invert the problem and obtain a suitable mapping that can be effectively used in fixed point theory to qualitatively analyze its solutions. In this paper we consider the existence of a positive sequence and utilize it in the capacity of integrating factor to obtain a new variation of parameters formula. Then, we will use the obtained new variation of parameters formula and revert to the contraction principle to arrive at results concerning, boundedness, periodicity and stability. The author is working on parallel results for the continuous case.

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*CUBO, A Mathematical Journal*,

*21*(3), 39–61. https://doi.org/10.4067/S0719-06462019000300039