Phi-Stable Operators And Inner Approximation-Solvability

We extend, by applying a theorem of Petryshyn (1970), the approximation-solvability of the nonlinear functional equations involving strongly stable Hilbert space mappings to the case of strongly ø-stablem appings—a new and rather general class of mappings. These mappings constitute a generalization of monotone mappings. Finally, we upgrade the obtained results to the case of Banach space mappings. © 1993 American Mathematical Society