Generalized Projection Operators in Banach Spaces: Properties and Applications
Ya. I. Alber
TL;DR
This paper reviews the properties and applications of generalized projection operators in Banach spaces, highlighting their role in solving variational inequalities and Wiener-Hopf equations.
Contribution
It provides a comprehensive account of metric and generalized projection operators in Banach spaces, including new connections to variational inequalities and Wiener-Hopf equations.
Findings
Established links between variational inequalities and Wiener-Hopf equations in Banach spaces.
Summarized properties of metric and generalized projection operators.
Extended applications of projection operators in functional analysis.
Abstract
This paper is an account (without proofs) of the results of our work "Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications", funct-an/9311001. The Section 9 establishing a connection between variational inequalities and Wienner-Hopf equations in Banach spaces by means of metric and generalized projection operators, is added.
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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Banach Space Theory · Point processes and geometric inequalities