Research Article
BibTex RIS Cite

Interpolative Kannan- Meir-Keeler type contraction

Year 2021, Volume: 5 Issue: 4, 611 - 614, 30.12.2021
https://doi.org/10.31197/atnaa.989389

Abstract

In this short manuscript, we revisit the renowned contraction’s of Meir-Keeler by involving the interpolation theory in the context of complete metric space. We provide a simple example to illustrate the validity of the observed result

References

  • 1] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae, 3 (1922), 133–181.
  • [2] P. Collaço, J. C. Silva, A complete comparison of 25 contraction conditions Nonlinear Analysis: Theory, Methods and Applications Volume 30, Issue 1, December 1997, Pages 471-476
  • [3] R. Kannan, Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71-76 (1968).
  • [4] R. Kannan, Some results on fixed points. II. Am. Math. Mon. 76, 405-408 (1969).
  • [5] E. Karapınar, Revisiting the Kannan type contractions via interpolation, Advances in the Teory of Nonlinear Analysis and Its Application, vol. 2, no. 2, pp. 85–87, 2018.
  • [6] A. Meir, E. Keeler, A theorem on contraction mappings. J. Math. Anal. Appl. 1969, 28, 326–329.
Year 2021, Volume: 5 Issue: 4, 611 - 614, 30.12.2021
https://doi.org/10.31197/atnaa.989389

Abstract

References

  • 1] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae, 3 (1922), 133–181.
  • [2] P. Collaço, J. C. Silva, A complete comparison of 25 contraction conditions Nonlinear Analysis: Theory, Methods and Applications Volume 30, Issue 1, December 1997, Pages 471-476
  • [3] R. Kannan, Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71-76 (1968).
  • [4] R. Kannan, Some results on fixed points. II. Am. Math. Mon. 76, 405-408 (1969).
  • [5] E. Karapınar, Revisiting the Kannan type contractions via interpolation, Advances in the Teory of Nonlinear Analysis and Its Application, vol. 2, no. 2, pp. 85–87, 2018.
  • [6] A. Meir, E. Keeler, A theorem on contraction mappings. J. Math. Anal. Appl. 1969, 28, 326–329.
There are 6 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Erdal Karapınar This is me

Publication Date December 30, 2021
Published in Issue Year 2021 Volume: 5 Issue: 4

Cite

Cited By