Abstract
We showed that the generalized contraction mapping defined on a closed convex subset of a weakly Cauchy normed space has a unique fixed point. Moreover, the sequence of iterates of any element in the domain of the given mapping is converging strongly to the fixed point of such a mapping.
Highlights
Rapid developments have occurred in many areas including variational and linear inequalities, optimization and applications in the field of approximation theory and minimum norm problems, with the help of the various applications of fixed points of the contraction mappings
Sahar Mohamed Ali, considered a contraction mapping defined on a closed convex subset of a weakly Cauchy normed space, spaces which are not necessarily be complete in general [7]
The following Theorem is a more generalization of Banach contraction principle in the case of weakly Cauchy normed space
Summary
Shimi, proved that a continuous mapping T which satisfy (2) on a non weakly compact convex subset C of a uniformly convex Banach space into itself with constants satisfy (1) has a fixed point [3]. Sahar Mohamed Ali, considered a contraction mapping defined on a closed convex subset of a weakly Cauchy normed space, spaces which are not necessarily be complete in general [7].
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