(untitled) (European Journal of Pure and Applied Mathematics, 2024)
The theory of monotone operators is fundamental in modern optimization and various areas of nonlinear analysis. Key classes of monotone operators include matrices with a positive semidefinite symmetric component and subdifferential operators. In this paper, we extend our investigation to displacement mappings. We derive formulas for set-valued and Moore-Penrose inverses. Additionally, we conduct a thorough examination of the operators (one-half times the identity plus T) and its inverse, providing a formula for the inverse of the operator. Our results are illustrated through an analysis of reflected and projection operators onto closed linear subspaces.