The split common fixed point problem for generalized demimetric mappings in two Banach spaces. (2nd January 2019)

• Record Type: Journal Article
• Authors: Takahashi, Wataru
• Is Part Of: Optimization. Volume 68:Number 1(2019)
• Page Start: 411
• Page End: 427
• Publication Date: 2019-01-02
• Subjects: Split common fixed point problem -- fixed point -- metric projection -- metric resolvent -- hybrid method -- shrinking projection method -- duality mapping; 47H05 -- 47H09; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1522637
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we consider the split common fixed point problem for new demimetric mappings in two Banach spaces. Using the hybrid method, we prove a strong convergence theorem for finding a solution of the split common fixed point problem in two Banach spaces. Furthermore, using the shrinking projection method, we obtain another strong convergence theorem for finding a solution of the problem in two Banach spaces. Using these results, we obtain well-known and new strong convergence theorems in Hilbert spaces and Banach spaces.