Perimetric Contraction on Quadrilaterals

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Published: Dec 17, 2025
Keywords:
Fixed point theorems Mapping contracting perimeter of triangles Perimetric contraction on quadrilaterals

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Anish Banerjee
Department of Mathematics, National Institute of Technology Durgapur, West Bengal 713209, India
Pratikshan Mondal
Department of Mathematics, A.B.N. Seal College, Cooch Behar, West Bengal 736101, India
Lakshmi Kanta Dey
Department of Mathematics, National Institute of Technology Durgapur, West Bengal 713209, India

Abstract

In this article, we introduce a four-point analogue of the Banach contraction principle and establish sufficient conditions for such mappings to possess fixed point(s) in complete metric spaces. Notably, the classical Banach contraction principle emerges as a special case of our results. We present several non-trivial examples that not only validate our theorems but also reveal that quadrilateral perimetric contractions need not imply other well-known contraction types. Furthermore, we extend our analysis to obtain fixed point theorems in non-complete metric spaces. Lastly, we address a recent result linking mappings contracting the perimeters of triangles in metric spaces to Banach-type contractions in 𝐚-metric spaces.

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How to Cite
Anish Banerjee, Pratikshan Mondal, & Lakshmi Kanta Dey. (2025). Perimetric Contraction on Quadrilaterals. Science & Technology Asia, 30(4), 55–67. retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/259111
Issue
Vol.30 No.4 (October-December 2025)
Section
Physical sciences
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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