Iterative methods for the split common fixed-point problem in Hilbert spaces

2014/10/25 by Huanhuan Cui, Fenghui Wang, Cui, Huanhuan +1 · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Fixed Point Theorems Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1410.6875

openalex publication_date 2014/10/25 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

The split common fixed-point problem is an inverse problem that consists in finding an element in a fixed-point set such that its image under a bounded linear operator belongs to another fixed-point set. Recently Censor and Segal proposed an efficient algorithm for solving such a problem. However, to employ their algorithm, one needs to know a prior information on the norm of the bounded linear operator. In this paper we propose a new algorithm that does not need any prior information of the operator norm, and we establish the weak convergence of the proposed algorithm under some mild assumptions.

Cited by

• Security Issues Associated With Error Correction And Privacy Amplification In Quantum Key Distribution

Related

• Split common fixed point problems and its variant forms
• The Problem of Split Equality Fixed-Point and its Applications
• On split common fixed point problem for multi-valued demicontractive mappings with multiple output sets in real Hilbert spaces
• The Split Common Null Point Problem
• New averaged type algorithms for solving split common fixed-point problem for demicontractive mappings