Taiwanese Journal of Mathematics

Cantor’s Theorem in 2-Metric Spaces and its Applications to Fixed Point Problems

B. K. Lahiri, Pratulananda Das, and Lakshmi Kanta Dey

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Abstract

2-metric space is an interesting nonlinear generalization of metric space which was conceived and studied in details by Gahler. In this paper, for the first time, we establish Cantor’s intersection theorem and Baire category theorem in 2-metric spaces. As a departure from normal practice we then apply Cantor’s theorem to establish some fixed point theorems in such spaces.

Article information

Source
Taiwanese J. Math., Volume 15, Number 1 (2011), 337-352.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406178

Digital Object Identifier
doi:10.11650/twjm/1500406178

Mathematical Reviews number (MathSciNet)
MR2780288

Zentralblatt MATH identifier
1245.54046

Subjects
Primary: 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20]

Keywords
$2$-metric spaces open ball boundedness closure Cantor's Theorem Baire's Theorem contractive mapping fixed point

Citation

Lahiri, B. K.; Das, Pratulananda; Dey, Lakshmi Kanta. Cantor’s Theorem in 2-Metric Spaces and its Applications to Fixed Point Problems. Taiwanese J. Math. 15 (2011), no. 1, 337--352. doi:10.11650/twjm/1500406178. https://projecteuclid.org/euclid.twjm/1500406178


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