Strong Convergence of New Algorithm for Monotone Operator in Banach Spaces

Abstract

Let E be a uniformly convex and uniformly smooth real Banach space with dual $E^{*}.$ The convergence of a new iterative algorithm for approximating zero points of monotone (not strongly monotone) and bounded mapping is established and analyzed. The algorithm is proved to converge strongly to $x^{*}\in A^{-1}(0)$ which is not involving the resolvent operator. Moreover, applications to solutions of variational inequality problems, convex minimization problems and a cluster of semi-pseudo mappings are included. Numerical results are reported to illustrate the behavior of the algorithm with different sequences of stepsizes and also to compare it with other algorithms.

Keywords:

• Monotone mappings
• zero point
• equilibrium problem
• strong convergence
• approximating

2000 MR SUBJECT CLASSIFICATION:

• 47H09
• 47H10
• 47L25

Authors’ contributions

All authors contributed equally to this work. All authors read and approved final manuscript.

Acknowledgments

The authors express their deep gratitude to the referee and the editor for his/her valuable comments and suggestions.

Disclosure statement

The authors declare that they have no competing interests.

Additional information

Funding

This article was funded by the National Science Foundation of China (11471059) and Science and Technology Research Project of Chongqing Municipal Education Commission (KJ1706154) and the Research Project of Chongqing Technology and Business University (KFJJ2017069).