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An Extension of Gregus Fixed Point Theorem
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AbstractLet "Equation missing" be a closed convex subset of a complete metrizable topological vector space "Equation missing" and "Equation missing" a mapping that satisfies "Equation missing" for all "Equation missing", where "Equation missing", "Equation missing", "Equation missing", "Equation missing", "Equation missing", and "Equation missing". Then "Equation missing" has a unique fixed point. The above theorem, which is a generalization and an extension of the results of several authors, is proved in this paper. In addition, we use the Mann iteration to approximate the fixed point of "Equation missing".
Title: An Extension of Gregus Fixed Point Theorem
Description:
AbstractLet "Equation missing" be a closed convex subset of a complete metrizable topological vector space "Equation missing" and "Equation missing" a mapping that satisfies "Equation missing" for all "Equation missing", where "Equation missing", "Equation missing", "Equation missing", "Equation missing", "Equation missing", and "Equation missing".
Then "Equation missing" has a unique fixed point.
The above theorem, which is a generalization and an extension of the results of several authors, is proved in this paper.
In addition, we use the Mann iteration to approximate the fixed point of "Equation missing".
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