2025/04/29 by A. B. Németh, Németh, A. B., S. Z. Németh +1 · 2 citations
Computer Science · Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2504.20773
openalex publication_date 2025/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper explores a natural generalization of Euclidean projection through the lens of strongly quasiconvex functions, as developed in prior works. By establishing a connection between strongly quasiconvex functions and the theory of mutually polar mappings on convex cones, we integrate this generalized projection concept into the duality framework of Riesz spaces, vector norms, and Euclidean metric projections. A central result of this study is the identification of conditions under which the null space of a projection onto a closed convex cone forms a closed convex cone. We provide a comprehensive characterization of such cones and projections, highlighting their fundamental role in extending the duality theory to generalized projection operators.