Strong convergence for gradient projection method and relatively nonexpansive mappings in Banach spaces

Kazuhide Nakajo

Applied Mathematics and Computation, 2015, vol. 271, issue C, 251-258

Abstract: Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space E, A be a single valued monotone and Lipschitz continuous mapping of C into E* and T be a single valued relatively nonexpansive mapping of C into itself. In this paper, we consider the composition and the convex combination of T and the gradient projection method for A which Goldstein (1964) proposed and proved the strong convergence to a common element of solutions of the variational inequality problem for A and fixed points of T by the hybrid method in mathematical programming (Haugazeau, 1968). And we get several results which improve the well-known results in a 2-uniformly convex and uniformly smooth Banach space and a Hilbert space.

Keywords: Gradient projection method; Variational inequality problem; Relatively nonexpansive mappings; 2-Uniformly convex Banach space; Hybrid method (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:271:y:2015:i:c:p:251-258

DOI: 10.1016/j.amc.2015.08.096

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