Derivation of Fixed-Point Theorem Using Expansive Mapping Approach

Vincent, Koech and Sammy, Musundi W. and Jeremiah, Kinyanjui (2023) Derivation of Fixed-Point Theorem Using Expansive Mapping Approach. Asian Research Journal of Mathematics, 19 (8). pp. 103-107. ISSN 2456-477X

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Abstract

Application of Fixed-Point Theorem has tremendously increased in different areas of interest and research. Fixed Point Theorem presents that if T:X→X is a contraction mapping on a complete metric space (X, d) then there exists a unique fixed point in X. A lot has been done on application of contraction mapping in Fixed Point Theorem on metric spaces such as Cantor set with the contraction constant of 1/3 , the Sierpinski triangle also with contraction constant of 1/2 . On the other hand, a mapping T:X → X on (X, d) such that ∀x, y ∈ X: d(Tx, Ty) ≥ d (x, y) is called an expansive mapping. There are various types of expansive mappings such as; isometry expansive mapping, proper/strict expansive mapping and anti-contraction expansive mapping. From the available literature, Fixed Point Theorem has been derived using contraction mapping approach. In this paper, we establish that it is also possible to derive Fixed Point Theorem using expansive mapping approach.

Item Type: Article
Subjects: AP Academic Press > Mathematical Science
Depositing User: Unnamed user with email support@apacademicpress.com
Date Deposited: 08 Jun 2023 05:41
Last Modified: 17 Oct 2024 03:57
URI: http://info.openarchivespress.com/id/eprint/1481

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