A New Fixed Point Theorem for Non-expansive Mappings and Its Application

2012/08/05 by Chunyan Yang, Yang Chunyan, Yang, Chunyan
Computer Science · Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA

paper · pdf · doi:10.48550/arxiv.1208.0979

arxiv created 2012/08/05 · openalex publication_date 2012/08/05 · arxiv updated 2012/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use KKM theorem to prove the existence of a new fixed point theorem for non-expansive mapping:Let M be a bounded closed convex subset of Hilbert space H, and A:M→ M be a non-expansive mapping, then exists a fixed point of A in M, we also apply this Theorem to study the solution for an integral equation,we can weak some conditions comparing with Banach's contraction principe.

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