An iterative viscosity approximation method for the split common fixed-point problem. (3rd June 2021)

• Record Type: Journal Article
• Authors: He, Huimin; Peng, Jigen; Fan, Qinwei
• Is Part Of: Optimization. Volume 70:Number 5/6(2021)
• Page Start: 1261
• Page End: 1274
• Publication Date: 2021-06-03
• Subjects: Split common fixed-point problem -- demicontractive operator -- viscosity approximation method -- strong convergence; 47J25 -- 47H45; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1819275
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The split common fixed point problem (SCFPP) for the demicontractive operators is studied. An iterative viscosity approximation method (VAM) for SCFPP is introduced. It is shown that the sequence generated by VAM is strongly convergent to a solution of SCFPP under certain conditions, and this solution is identified to be the unique solution of some variational inequality. The main result of this paper extends and improves 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 Theory Appl. 2014;183], Boikanyo [A strongly convergent algorithm for the split common fixed point problem. Appl Math Comput. 2015;265:844–853] and Cui–Wang [Iterative methods for the split common fixed point problem in Hilbert spaces. Fixed Point Theory Appl. 2014;78].