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Acta Mathematica Vietnamica

ON THE RATIONAL RECURSIVE SEQUENCE xn+1=A+α0xn+α1xnσB+β0xn+β1xnτ

E. M. E. ZAYED, M. A. EL-MONEAM

Abstract

The main objective of this paper is to study the boundedness, the periodicity, the convergence and the global stability of the positive solutions of the difference equation xn+1=A+α0xn+α1xnσB+β0xn+β1xnτ,  n=0,1,2, where the coefficients A,B,α0,α1,β0,β1(0,) and σ,τN. The initial conditions xω,,x1,x0 are arbitrary positive real numbers and ω=max{τ,σ}. Some numerical examples are presented.