On the monotonicity properties of additive representation functions, II

For a set AA of positive integers and any positive integer nn, let R1(A,n)R1(A,n), R2(A,n)R2(A,n) and R3(A,n)R3(A,n) denote the number of solutions of a+a′=na+a′=n with the additional restriction a,a′∈Aa,a′∈A; a,a′∈A,a