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Numerical Algorithms

, Volume 81, Issue 3, pp 853–878 | Cite as

New semi-implicit midpoint rule for zero of monotone mappings in Banach spaces

  • Yan TangEmail author
  • Zhiqing Bao
Open Access
Original Paper
  • 114 Downloads

Abstract

Let E be a nonempty closed uniformly convex and 2-uniformly smooth Banach space with dual E and A : EE be Lipschitz continuous monotone mapping with A− 1(0) ≠ ∅. A new semi-implicit midpoint rule (SIMR) with the general contraction for monotone mappings in Banach spaces is established and proved to converge strongly to xE, where JxA− 1(0). Moreover, applications to convex minimization problems, solution of Hammerstein integral equations, and semi-fixed point of a cluster of semi-pseudo mappings are included.

Keywords

Semi-implicit Monotone mappings Zero point Viscosity approximation 

Mathematics Subject Classification (2010)

47H09 47H10 47L25 

Notes

Acknowledgements

The authors express their deep gratitude to the referees and the editor for their valuable comments and suggestions.

Author Contributions

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

Funding information

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).

Compliance with Ethical Standards

Competing Interests

The authors declare that they have no competing interests.

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsChongqing Technology and Business UniversityChongqingChina

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