Convergence Theorems for Modified Implicit Iterative Methods with Perturbation for Pseudocontractive Mappings

Jong Soo Jung
Additional contact information
Jong Soo Jung: Department of Mathematics, Dong-a University, Busan 49315, Korea

Mathematics, 2020, vol. 8, issue 1, 1-16

Abstract: In this paper, first, we introduce a path for a convex combination of a pseudocontractive type of mappings with a perturbed mapping and prove strong convergence of the proposed path in a real reflexive Banach space having a weakly continuous duality mapping. Second, we propose two modified implicit iterative methods with a perturbed mapping for a continuous pseudocontractive mapping in the same Banach space. Strong convergence theorems for the proposed iterative methods are established. The results in this paper substantially develop and complement the previous well-known results in this area.

Keywords: modified implicit iterative methods with perturbed mapping; pseudocontractive mapping; strongly pseudocontractive mapping; nonexpansive mapping; weakly continuous duality mapping; fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/1/72/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/1/72/ (text/html)

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:gam:jmathe:v:8:y:2020:i:1:p:72-:d:304699

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().