Interpolative Kannan- Meir-Keeler type contraction

Year 2021, , 611 - 614, 30.12.2021

Erdal Karapınar

https://doi.org/10.31197/atnaa.989389

Cited By: 14

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

Keywords

Contraction, İnterpolation, Banach contraction, Meir-Keeler contraction, Kannan contraction

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.