On the difference equation yn+1=α+βe-ynγ+yn-1

In this paper, we investigate the convergence, the boundedness and the periodic character of the positive solutions of the difference equationyn+1=α+βe-ynγ+yn-1,n=0,1,2,…,where the parameters α, β, γ are positive numbers and the initial conditions y−1, y0 are arbitrary non-negative numbers.