\cal T-class algorithms for pseudocontractions and κ-strict pseudocontractions in Hilbert spaces

2007/12/04 by Jean‐Philippe Chancelier, Jean-Philippe Chancelier, Chancelier, Jean-Philippe
Computer Science · Mathematics · #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Fixed Point Theorems Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.OC

paper · pdf · doi:10.48550/arxiv.0712.0528

arxiv created 2007/12/04 · openalex publication_date 2007/12/04 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper we study iterative algorithms for finding a common element of the set of fixed points of κ-strict pseudocontractions or finding a solution of a variational inequality problem for a monotone, Lipschitz continuous mapping. The last problem being related to finding fixed points of pseudocontractions. These algorithms were already studied in [G.L. Acedo, H.-K. Xu] and [N. Nadezhkina, W. Takahashi] but our aim here is to provide the links between these know algorithms and the general framework of \cal T-class algorithms studied in [H.H. Bauschke, P.L. Combettes].

Related

• Strict pseudocontractions and demicontractions, their properties and applications
• Weak and strong convergence theorems for enriched strictly pseudocontractive operators in Hilbert spaces
• Weak Convergence Theorem by a New Extragradient Method for Fixed Point Problems and Variational Inequality Problems
• Solution of variational inequality problems on fixed point sets of nonexpansive mappings using iterative methods
• Quantitative results on the Ishikawa iteration of Lipschitz pseudo-contractions