A New Construction and Convergence Analysis of Non-Monotonic Iterative Methods for Solving ρ -Demicontractive Fixed Point Problems and Variational Inequalities Involving Pseudomonotone Mapping

Chainarong Khunpanuk, Bancha Panyanak and Nuttapol Pakkaranang
Additional contact information
Chainarong Khunpanuk: Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand
Bancha Panyanak: Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Nuttapol Pakkaranang: Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand

Mathematics, 2022, vol. 10, issue 4, 1-29

Abstract: Two new inertial-type extragradient methods are proposed to find a numerical common solution to the variational inequality problem involving a pseudomonotone and Lipschitz continuous operator, as well as the fixed point problem in real Hilbert spaces with a ρ -demicontractive mapping. These inertial-type iterative methods use self-adaptive step size rules that do not require previous knowledge of the Lipschitz constant. We also show that the proposed methods strongly converge to a solution of the variational inequality and fixed point problems under appropriate standard test conditions. Finally, we present several numerical examples to show the effectiveness and validation of the proposed methods.

Keywords: variational inequalities; fixed point problem; subgradient extragradient method; strong convergence; tseng’s extragradient method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/4/623/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/4/623/ (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:10:y:2022:i:4:p:623-:d:752017

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 ().