Solvable Three-Dimensional Product-Type System of Difference Equations with Multipliers

Abstract

The solvability of the following three-dimensional product-type system of difference equations xn+1=αyanzbn−1, yn+1=βzcnxdn−1, zn+1=γxfnygn−1, n∈N0, where a,b,c,d,f,g∈Z,α,β,γ∈C\{0} and x−i, y−i, z−i∈C\{0}, i∈{0, 1}, is shown. This is the first three-dimensional system of the type with multipliers for which formulas are presented for their solutions in closed form in all the cases.