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- Title
A New Construction and Convergence Analysis of Non-Monotonic Iterative Methods for Solving ρ -Demicontractive Fixed Point Problems and Variational Inequalities Involving Pseudomonotone Mapping.
- Authors
Khunpanuk, Chainarong; Panyanak, Bancha; Pakkaranang, Nuttapol
- 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.
- Subjects
VARIATIONAL inequalities (Mathematics); MONOTONE operators; HILBERT space; SUBGRADIENT methods
- Publication
Mathematics (2227-7390), 2022, Vol 10, Issue 4, pN.PAG
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math10040623