Strong convergence theorem for common zero points of inverse strongly monotone mappings and common fixed points of generalized demimetric mappings

Abstract

In this paper, we introduce a new and efficient algorithm for finding a common element of the set of common fixed points of a finite family of generalized demimetric mappings and the set of common zero points of a finite family of inverse strongly monotone mappings in Hilbert spaces. Strong convergence of the proposed algorithm is established under standard and mild conditions in a Hilbert space. As an application, we use our algorithm for solving the common solutions to the variational inequality problem, the common minimization problem, the multiple-set split feasibility problem, the split common fixed point problem and the split common null point problem.

Keywords:

• Generalized demimetric mappings
• inverse strongly monotone
• variational inequality
• multiple-set split feasibility problem

2000 Mathematics Subject Classifications:

• 47H09
• 47J20
• 49J30

Acknowledgments

The author would like to thank the referees and the editor for their many useful comments and helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).