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NOTES ON ORTHOGONAL-COMPLETE METRIC SPACES

Published online by Cambridge University Press:  11 May 2021

NGUYEN VAN DUNG*
Affiliation:
Department of Mathematics and Information Technology Teacher Education, Dong Thap University, Cao Lanh City, Dong Thap Province, Vietnam

Abstract

We prove that the restriction of a given orthogonal-complete metric space to the closure of the orbit induced by the origin point with respect to an orthogonal-preserving and orthogonal-continuous map is a complete metric space. Then we show that many existence results on fixed points in orthogonal-complete metric spaces can be proved by using the corresponding existence results in complete metric spaces.

Type
Research Article
Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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