On the solution of nonsmooth generalized equations (Q2912553)

For approximating a locally unique solution \(x^*\) of the nonsmooth generalized equation NEWLINE\[NEWLINE0\in f(x)+ F(x),NEWLINE\]NEWLINE where \(f\) is an operator defined on an open subset \(D\) of a Banach space \(X\) with values in a Banach space \(Y\) and \(F\) denotes a set valued map from \(X\) to the subsets of \(Y\) the author considers the method NEWLINE\[NEWLINE0\in A(x_n, x_{n+1})+ F(x_{n+1})\quad (n\geq 0),NEWLINE\]NEWLINE where \(A: D\times D\to Y\) is an approximation of the operator \(f\) satisfying certain properties. By using more precise estimates and weaker hypothesis, a finer convergence analysis than before with the advantages such as larger convergence radius and more precise error estimates is provided.