The recurrent sequences of inequalities

Abstract

Consider the sequence of inequalities Oi,k+1 sifj(o i,t ,..., a„ k)) + bi k, j=i i = 1 , 2 , n, k = 0,1,2, where r is a concave and increasing function and the functions j, i , j = 1 satisfy some additional conditions ((2.2) and (2.3)). In this note we give an answer to the following question: under what assumptions regarding the given sequences {£>;,*} their behaviour implies a similar one for the sequences {a,,*}.