Weak and strong convergence theorems for the split common fixed point problem with demicontractive operators. (3rd June 2021)

• Record Type: Journal Article
• Authors: Fan, Qinwei; Peng, Jigen; He, Huimin
• Is Part Of: Optimization. Volume 70:Number 5/6(2021)
• Page Start: 1409
• Page End: 1423
• Publication Date: 2021-06-03
• Subjects: Split common fixed point problem -- demicontractive mapping -- weak convergence -- strong convergence; 47J25 -- 47H45; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1890074
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : A novel iterative algorithm is introduced for solving the split common fixed point problem with demicontractive operators. Weak and strong convergence of the algorithm is discussed. The step-sizes of the algorithm are chosen in such a way that the implementation of the algorithm does not depend on operator norms. The main results proven in this paper extend and improve some results of Yao et al. [Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem. Fixed Point Theor Appl. 2014;2014:183], Boikanyo [A strongly convergent algorithm for the split common fixed point problem. Appl Math Comput. 2015;265:844–853] and Cui and Wang [Iterative methods for the split common fixed point problem in Hilbert spaces. Fixed Point Theor Appl. 2014;2014:78].