Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

A NEW STUDY IN EUCLID'S METRIC SPACE CONTRACTION MAPPING AND PYTHAGOREAN RIGHT TRIANGLE RELATIONSHIP

  • SAEED A.A. AL-SALEHI (Department of Mathematics, Aden University) ;
  • MOHAMMED M.A. TALEB (Department of Mathematics, Hodeidah University) ;
  • V.C. BORKAR (Department of Mathematics, Yeshwant Mahavidyalaya, Swami Ramanand Teerth Marathwada University)
  • Received : 2023.10.21
  • Accepted : 2023.12.07
  • Published : 2024.03.30
Download PDF
⟨ Previous Next ⟩

Abstract

Our study explores the connection between the Pythagorean theorem and the Fixed-point theorem in metric spaces. Both of which center around the concepts of distance transformations and point relationships. The Pythagorean theorem deals with right triangles in Euclidean space, emphasizing distances between points. In contrast, fixed-point theorems pertain to the points that remain unchanged under specific transformations thereby preserving distances. The article delves into the intrinsic correlation between these concepts and presents a novel study in Euclidean metric spaces, examining the relationship between contraction mapping and Pythagorean Right Triangles. Practical applications are also discussed particularly in the context of image compression. Here, the integration of the Pythagorean right triangle paradigm with contraction mappings results in efficient data representation and the preservation of visual data relation-ships. This illustrates the practical utility of seemingly abstract theories in addressing real-world challenges.

Keywords

Acknowledgement

The Authors are thankful to the anonymous referee's for their valuable comments towards the improvement of paper.

References

  1. S. Swaminathan, The Pythagorean theorem, Journal of Biodiversity, Bioprospecting and Development 1 (2014), 1-4.
  2. R.P. Agarwal, Pythagorean theorem before and after Pythagoras, Advanced Studies in Contemporary Mathematics 30 (2020), 357-389.
  3. A.L. Shields, Pythagorean Theorem: Proof and Applications, Proceedings of the American Mathematical Society 5 (1964), 703-706.
  4. S. Park, Ninety Years of the Brouwer Fixed Point Theorem, Vietnam Journal of Mathematics 27 (1999), 187-222.
  5. V. Brattka, S. Le Roux, J.S. Miller and A. Pauly, Connected choice and the Brouwer fixed point theorem, Journal of Mathematical Logic 19 (2019), 1950004.
  6. M. Jleli and B. Samet, A new generalization of the Banach contraction principle, Journal of Inequalities and Applications 2014 (2014), 1-8. https://doi.org/10.1186/1029-242X-2014-1
  7. S. Weng and Q. Zhu, Some Fixed-Point Theorems on Generalized Cyclic Mappings in B-Metric-Like Spaces, Complexity 2021 (2021), 1-7.
  8. R.P. Agarwal, Pythagorean Triples before and after Pythagoras, Computation 2 (2020), 62.
  9. P. Das, L.K. Dey, Fixed point of contractive mappings in generalized metric spaces, Mathematica Slovaca 59 (2009), 499-504. https://doi.org/10.2478/s12175-009-0143-2