A note on the nonautonomous Beverton-Holt model

In this paper, we study the asymptotic behavior of positive solutions of nonautonomous Beverton-Holt equation where {K n } is a positive persistent and bounded sequence. In our main result, we proved that all positive solutions {x n } satisfy the inequality The obtained result represents the extension of the Cushing-Hensons's conjecture. Applications to the case when {K n } is a positive periodic sequence are given and the alternative proof of the Cushing-Henson's conjecture is also presented.