On the solvability of relaxed one-sided Lipschitz inclusions in Hilbert spaces

TL;DR

This paper establishes solvability conditions for relaxed one-sided Lipschitz multivalued mappings in Hilbert spaces, explores inverse properties, and analyzes convergence of a numerical scheme for algebraic inclusions.

Contribution

It introduces new solvability theorems for relaxed one-sided Lipschitz inclusions in Hilbert spaces and studies inverse and convergence properties.

Findings

Proved solvability theorems for relaxed one-sided Lipschitz mappings

Derived properties of inverses of such mappings

Analyzed convergence of a numerical scheme for algebraic inclusions

Abstract

We prove solvability theorems for relaxed one-sided Lipschitz multivalued mappings in Hilbert spaces and for composed mappings in the Gelfand triple setting. From these theorems, we deduce properties of the inverses of such mappings and convergence properties of a numerical scheme for the solution of algebraic inclusions.