Existence theorems of solutions for a system of nonlinear inclusions with an application (Q2471902)

Let \(E\) be a real Banach space and \(X\) be a nonempty subset of \(E\). Let \(A,B:X\times X\to E\), \(g:X\to E\) be nonlinear mappings and let \(S,T:X\to 2^{X}\) be two set-valued mappings. In this paper, the authors study the problem of finding \(u\in X\), \(x\in Su\), \(y\in Tu\) such that \[ A(y,x)=gu,\quad B(x,y)=gu. \] By using the iterative technique and Nadler's theorem, the authors construct a new iterative algorithm and prove the existence of solutions for the above system and the convergence of the sequences generated by the algorithm. As an application, they show the existence of a solution for a system of functional equations arising in dynamic programming of multistage decision processes.