Approximation of common fixed points of a countable family of relatively nonexpansive mappings. (English) Zbl 1202.47068
Summary: We introduce two general iterative schemes for finding a common fixed point of a countable family of relatively nonexpansive mappings in a Banach space. Under suitable assumptions, we not only obtain several convergence theorems announced by many authors, but also prove them under weaker assumptions. Applications to the problem of finding a common element of the fixed point set of a relatively nonexpansive mapping and the solution set of an equilibrium problem are also discussed.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
general iterative schemes; family of nonexpansive mappings in Banach space; convergence theoremsReferences:
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