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Abstract
In this paper, we study some facts concerning the topological structures of some subsets of a given normed space, prove the existence of a unique fixed point of r-contraction mappings defined on cartesian product of a closed and weakly Cauchy subset of a weakly complete normed space, propose an iterated sequence that converges strongly to such a unique fixed point, and prove the existence of fixed points of nonexpansive mapping defined on cartesian product of a closed and sequentially Cauchy subset of a weakly complete normed space.
How to Cite this Article:
Sahar Mohamed Ali Abou Bakr, E.M. El-Shobaky, Fixed point theorems for contraction and nonexpansive mappings defined on Cartesian products spaces, Communications in Optimization Theory 2014 (2014), Article ID 10.