Convergence theorems of subgradient extragradient algorithm for solving variational inequalities and a convex feasibility problem

Let C be a nonempty closed and convex subset of a uniformly smooth and 2-uniformly convex real Banach space E with dual space E ∗ . In this paper, a Krasnoselskii-type subgradient extragradient iterative algorithm is constructed and used to approximate a common element of solutions of variational in...

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Published in:Fixed point theory and algorithms for sciences and engineering Vol. 2018; no. 1; pp. 1 - 14
Main Authors: Chidume, C. E., Nnakwe, M. O.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 18.06.2018
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Banach spaces
Differential Geometry
Fixed points (mathematics)
Iterative algorithms
Iterative Methods and Optimization Algorithms: A Dedication to Dr. Hong-Kun Xu
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Relatively nonexpansive maps
Subgradient extragradient algorithm
Theorems
Topology
Variational inequality
47H10
47J20
Variational inequality
47H09
Relatively nonexpansive maps
47J05
Subgradient extragradient algorithm
47J25
ISSN:1687-1812, 1687-1812, 2730-5422
Online Access:Get full text
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Summary:Let C be a nonempty closed and convex subset of a uniformly smooth and 2-uniformly convex real Banach space E with dual space E ∗ . In this paper, a Krasnoselskii-type subgradient extragradient iterative algorithm is constructed and used to approximate a common element of solutions of variational inequality problems and fixed points of a countable family of relatively nonexpansive maps. The theorems proved are improvement of the results of Censor et al. (J. Optim. Theory Appl. 148:318–335, 2011 ).
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content type line 14
ISSN:1687-1812
1687-1812
2730-5422
DOI:10.1186/s13663-018-0641-4