Closed form expression of tractable semi-max-type two-dimensional system of difference equations with variable coefficients

Author

Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

Abstract

In this paper we shall examine the periodicity and formularization of the solutions for a
system of semi-max-type difference equations of second order in the form
x n +1 = max

A n
y n −1
, x n −1

,
y n +1 = min

B n
x n −1
, y n −1

,
n ∈ N 0 , where N 0 = N ∪ { 0 } , (A n ) n ∈ N 0 and (B n ) n ∈ N 0 are two-periodic positive sequences, and initial
values x 0 , x −1 , y 0 , y −1 ∈ (0 , + ∞ ) .

Keywords