Rus-Hicks-Rhoades maps on quasi-metric spaces revisited

Authors

  • Salvador Romaguera Universitat Politècnica de Valencia Corresponding Author

Keywords:

Quasi-metric space, Metric spaces

Abstract

Motivated by recent researches conducted by Sehie Park, we here present various adjustments and clarifications concerning the quasi-metric extension of well-known fixed point theorems due to Rus, and Hicks and Rhoades, respectively. In particular, some pertinent examples are given.

References

[1] H. Aydi, M. Jleli, E. Karapinar, On fixed point results for α-implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal. Model. Control 21 (2016) 40–56.

[2] S. Cobzaş, Functional Analysis in Asymmetric Normed Spaces, Frontiers in Mathematics, Birkhäuser/Springer Basel AG: Bael, Switzerland, 2013.

[3] P. Fletcher, W.F. Lindgren, Quasi-Uniform Spaces, Marcel Dekker, Inc. New York, NY, USA; Basel, Switzerland, 1982.

[4] M. Jleli, B. Samet, Remarks on G-metric spaces and fixed point theorems, Fixed Point Theory Appl. 2012:210, 2012.

[5] T.L. Hicks, B.E. Rhoades, A Banach type fixed point theorem, Math. Japon. 24 (1979) 327–330

[6] S. Park, Almost all about Rus-Hicks-Rhoades maps in quasi-metric spaces, Adv. Theory Nonlinear Anal. Appl. 7 (2023), 455-472.

[7] S. Park, All metric fixed point theorems hold for quasi-metric spaces, Results Nonlinear Anal. 6 (2023), 116–127.

[8] S. Park, Some applications of the Weak Contraction Principle, Lett. Nonlinear Anal. Appl. 3 (2025), 1-4

[9] S. Romaguera, Remarks on the fixed point theory for quasi-metric spaces, Results Nonlinear Anal. Appl. 7 (2024), 70–74.

[10] S. Romaguera, A short note on the article “Some Applications of the Weak Contraction Principle”, Lett. Nonlinear Anal. Appl.3 (2025), 103-104.

[11] I.A. Rus, Teoria punctului fix în analiza funcţională, Babeş-Bolyai University, Cluj-Napoca, 1973.

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Published

2025-04-03

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