Global asymptotic stability of a higher order nonlinear difference equation

A potent approach of subsequence analysis is introduced in this work, for investigating the following equation: xn=xn−kbxn−m+xn−lb+axn−kb+xn−mxn−lb+a,n=1,2,…, where k,m,lk,m,l are positive integers, xs,xs+1,…,x0∈(0,∞),s=min{1−k,1−m,1−l},a,b≥0xs,xs+1,…,x0∈(0,∞),s=min{1−k,1−m,1−l},a,b≥0. The global asymptotical stability of the above equation is verified, which extends and includes many corresponding results obtained in the cited references.