Abstract
AbstractWe are concerned with the problem of solving variational inequalities which are defined on the set of fixed points of a multivalued nonexpansive mapping in a reflexive Banach space. Both implicit and explicit approaches are studied. Strong convergence of the implicit method is proved if the space satisfies Opial’s condition and has a duality map weakly continuous at zero, and the strong convergence of the explicit method is proved if the space has a weakly continuous duality map. An essential assumption on the multivalued nonexpansive mapping is that the mapping be single valued on its nonempty set of fixed points.
Funder
Università della Calabria
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Geometry and Topology,Modelling and Simulation
Reference40 articles.
1. Goebel, K., Reich, S.: Uniform convexity, hyperbolic geometry, and nonexpansive mappings. Dekker, New York (1984)
2. Nadler, S.: Multi-valued contraction mappings. Pac. J. Math. 30(2), 475–488 (1969)
3. Lami, Dozo E.: Multivalued nonexpansive mappings and Opial condition. Proc. Am. Math. Soc. 38(2), 286–292 (1973)
4. Lim, T.C.: A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space. Bull. Am. Math. Soc. 80(6), 1123–1126 (1974)
5. Ko, H.M.: Fixed point theorems for point-to-set mappings and the set of fixed points. Pac. J. Math. 42(2), 369–379 (1972)
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