Several iterative algorithms for solving the split common fixed point problem of directed operators with applications

Abstract

In this paper, we propose a new simultaneous iterative algorithm for solving the split common fixed point problem of directed operators. Inspired by the idea of cyclic iterative algorithm, we also introduce two iterative algorithms which combine the process of cyclic and simultaneous together. Under mild assumptions, we prove convergence of the proposed iterative sequences. As applications, we obtain several iteration schemes to solve the inverse problem of multiple-sets split feasibility problem. Numerical experiments are presented to confirm the efficiency of the proposed iterative algorithms.

Keywords:

• split common fixed point problem
• directed operators
• simultaneous

AMS Subject Classifications:

• 47J25
• 47N10
• 65J15
• 90C25

Notes

This work was supported by the National Natural Science Foundations of China [grant number 11131006], [grant number 11201216], [grant number 11401293], [grant number 11461046]; the National Basic Research Program of China [grant number 2013CB329404]; the Natural Science Foundations of Jiangxi Province [grant number 20142BAB211016]; and the Science Funds of The Education Department of Jiangxi Province [grant number GJJ13012], [grant number GJJ14124].