The study suggests asymptotic behavior of the solution to a new class of difference equations: . where a, bi, Ã?± and Ã?² are positive real numbers for i = 0, 1, Ã?· Ã?· Ã?· , k , and the initial conditions ÃË?-j, ÃË?-j+1, Ã?· Ã?· Ã?·, ÃË?0 are randomly positive real numbers where j = 2k + 1. Accordingly, we consider the stability, boundedness and periodicity of the solutions of this recursive sequence. Indeed, we give some interesting counter examples in order to verify our strong results.
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