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NOTES ON ORTHOGONAL-COMPLETE METRIC SPACES

Part of: Nonlinear operators and their properties Spaces with richer structures

Published online by Cambridge University Press:  11 May 2021

NGUYEN VAN DUNG Open the ORCID record for NGUYEN VAN DUNG [Opens in a new window]
NGUYEN VAN DUNG*
Affiliation:
Department of Mathematics and Information Technology Teacher Education, Dong Thap University, Cao Lanh City, Dong Thap Province, Vietnam
*
e-mail: nvdung@dthu.edu.vn
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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.

Keywords

complete metric spacefixed pointorthogonal-completeorthogonal set

MSC classification

Primary: 47H10: Fixed-point theorems
Secondary: 54E99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 1 , February 2022 , pp. 154 - 160
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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