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Journals / Advances in the Theory of Nonlinear Analysis and its Application / 2021 / Cilt: 5 Sayı: 4

Interpolative Kannan- Meir-Keeler type contraction

Erdal Karapınar(CANKAYA UNIVERSITY)
Pages
611–614
Publication Date
2021-12-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We provide a simple example to illustrate the validity of the observed result

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:We provide a simple example to illustrate the validity of the observed result
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Contraction · İnterpolation · Banach contraction

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

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Cite This Article

Karapınar, E. (2021). Interpolative Kannan- Meir-Keeler type contraction. Advances in the Theory of Nonlinear Analysis and its Application, Cilt: 5 Sayı: 4, 611–614. https://doi.org/10.31197/atnaa.989389

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References (6)

  1. 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.