Weak and Strong Convergence Theorems for New Demimetric Mappings and the Split Common Fixed Point Problem in Banach Spaces. (27th July 2018)

• Record Type: Journal Article
• Authors: Takahashi, Wataru
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 10(2018)
• Page Start: 1011
• Page End: 1033
• Publication Date: 2018-07-27
• Subjects: Fixed point -- Halpern iteration procedure -- Mann iteration procedure -- metric projection -- metric resolvent -- split common fixed point problem; 47H05 -- 47H09; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1466803
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we consider the split common fixed point problem for new demimetric mappings in Banach spaces. Using the idea of Mann's iteration, we prove a weak convergence theorem for finding a solution of the split common fixed point problem in Banach spaces. Furthermore, using the idea of Halpern's iteration, we obtain a strong convergence theorem for finding a solution of the problem in Banach spaces. Using these results, we obtain well-known and new weak and strong convergence theorems in Hilbert spaces and Banach spaces.