General algorithms for split common fixed point problem of demicontractive mappings

Abstract

In the first part of this paper, we present a new general algorithm for solving the split common fixed point problem for an infinite family of demicontractive mappings. We establish strong convergence of the algorithm in an infinite dimensional Hilbert space. As applications, we consider algorithms for split variational inequality problem and split common null point problem. In the second part of this paper, we present a new algorithm and strong convergence theorem for approximation of solutions of split equality fixed point problems for an infinite family of demicontractive mappings. Our results improve and generalize some recent results in the literature.

Keywords:

• split common fixed point problems
• split equality fixed point problems
• split variational inequality problem
• demicontractive mapping

AMS Subject Classifications:

• 47J25
• 47N10
• 65J15
• 90C25

Acknowledgements

The author would like to thank the referees for their comments and suggestions on improving an earlier version of this paper.

Notes

No potential conflict of interest was reported by the author.