Abstract
In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping and the set of solutions of a variational inequality in a Banach space. Our results extend and improve the recent ones announced by Li (J Math Anal Appl 295:115–126, 2004), Jianghua (J Math Anal Appl 337:1041–1047, 2008), and many others.
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Liu, Y. Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings. J Glob Optim 46, 319–329 (2010). https://doi.org/10.1007/s10898-009-9427-x
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DOI: https://doi.org/10.1007/s10898-009-9427-x
Keywords
- Variational inequalities
- Relatively weak nonexpansive mappings
- Generalized projection
- Cauchy sequences
- Continuity