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Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces. (English) Zbl 1088.47054

Motivated by D. Butnariu, S. Reich and A. J. Zaslavski [J. Appl. Anal. 7, No. 2, 151–174 (2001; Zbl 1010.47032)], the authors establish weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces by using a suitable iterative sequence defined via the concept of generalized projection. Applications to convex feasibility problems and to a proximal-type algorithm for monotone operators in Banach spaces are also given.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H05 Monotone operators and generalizations

Citations:

Zbl 1010.47032
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