Strong convergence theorems for relatively nonexpansive mappings and Lipschitz-continuous monotone mappings in Banach spaces

Ying Liu () and Hang Kong ()
Additional contact information
Ying Liu: Hebei University
Hang Kong: Hebei University

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 4, 1049-1065

Abstract: Abstract In this paper, we introduce an iterative process for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for a Lipschitz-continuous, monotone mapping in a Banach space. We obtain a strong convergence theorem for three sequences generated by this process. Our results improve and extend the corresponding results announced by many others. A simple numerical example is given to support our theoretical results.

Keywords: Relatively nonexpansive mapping; generalized projection; monotone mapping; variational inequality; 2-uniformly convex (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-019-0373-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:50:y:2019:i:4:d:10.1007_s13226-019-0373-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-019-0373-0

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().