On solution sets of nonlinear equations with nonsmooth operators in Hilbert space and the quasi-solution method (Q2020464)

The author investigates nonlinear irregular equations in Hilbert space with a~priori constraints, without assuming differentiability for the governing operator. The constraints are described by a bounded closed set that is part of an extended source representation class expressed in terms of a given linear operator. The unique solvability of the problem is not assumed. It is established that solutions to the problem form a cluster of diameter strictly less than the one of the constraints set. The approximation properties of the quasi-solution method are addressed in relation to the solution set of the original problem.