On a General Non-Linear Difference Equation of Third-Order

In this paper, we investigate the following general difference equations {equation*} xₙ₊₁=h⁻¹( h( xₙ) {Ah( xₙ₋₁)+Bh( xₙ₋₂) }{Ch( xₙ₋₁)+Dh( xₙ₋₂)}) ,\ n∈ N₀, {equation*} where the parameters $A, B, C, D$ and the initial values x-Φ, for Φ=0,2̄ are real numbers, h is a continuous and strictly monotone function, h( R) =R, h( 0) =0. In addition, we obtain closed-form solutions of aforementioned difference equations. Finally, numerical applications are given.