Additional Studies on Displacement Mapping with Restrictions
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i4.5504Keywords:
Displacement mapping, maximally monotone operator, nonexpansive mapping, , Moore-Penrose inverse set-valued inverse, inverse, Yosida approximation.Abstract
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.
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Copyright (c) 2024 Salihah Alwadani
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