A convergence result for second order difference equations of monotone type (Q2919582)

The paper is concerned with the second-order difference problem NEWLINE\[NEWLINE\left\{ \begin{aligned} & u_{i+1}-(1+\theta_i)u_i+\theta_iu_{i-1}\in c_iAu_i+f_i,\;1\leq i\leq N,\\ & u_0=a,\;u_{N+1}-u_N\in -\beta(u_{N+1}-b), \end{aligned}\right.NEWLINE\]NEWLINE where \(A:D(A)\subseteq H\to H\) and \(\beta:D(\beta)\subseteq H\to H\) are maximal monotone operators (possibly multivalued), \(H\) is a real Hilbert space, and \(a,\,b\in H\), \(f_i\in H\), \(c_i>0\), \(\theta_i\in (0,1)\) for all \(i=1,\dots, N\) are given elements. The authors study the continuous dependence on data for the above problem, where the investigated sequence of operators is convergent in the sense of the resolvent. An application to difference-differential equations is also presented.