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Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space. (English) Zbl 1137.47056
Summary: We establish strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space by using the hybrid method in mathematical programming. Our results extend and improve the recent ones announced by S.-Y. Matsushita and W. Takahashi [J. Approximation Theory 134, No. 2, 257–266 (2005; Zbl 1071.47063)], C. Martinez-Yanes and H.-K. Xu [Nonlinear Anal., Theory Methods Appl. 64, No. 11 (A), 2400–2411 (2006; Zbl 1105.47060)], and many others.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties