SciELO - Scientific Electronic Library Online

 
vol.39 issue2Non-linear new product A ∗ B − B ∗ A derivations on ∗-algebras author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

  • On index processCited by Google
  • Have no similar articlesSimilars in SciELO
  • On index processSimilars in Google

Share


Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.2 Antofagasta Apr. 2020

http://dx.doi.org/10.22199/issn.0717-6279-2020-02-0030 

Artículos

Fixed points and diametral sets for sequentially bounded mappings in orbital ultrametric spaces

1University Moulay Ismail, Dept. of Mathematics, Faculty of Sciences, Meknes, Morocco. e-mail: m.babahmed@fs.umi.ac.ma

2University Moulay Ismail, Dept. of Mathematics, Faculty of Sciences, Meknes, Morocco. e-mail: abdelkhalek.elamrani@usmba.ac.ma

3University Sidi Mohamed Ben Abdellah, Dept. of Mathematics, FSDM, LAMA, Fes, Morocco. e-mail: samih.lazaiz@usmba.ac.ma

Abstract

In this paper, the T -orbital ultrametric spaces are introduced and a fixed point theorem for sequentially bounded mappings is given. Our main result extends some known theorems for nonexpansive mappings. Examples are given to support our work.

Keywords: Ultrametric spaces; T -orbital sets; T -dimetral sets; Fixed point; Sequentially bounded mappings

Texto completo disponible sólo en PDF

Full text available only in PDF format.

References

[1] S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales”, Fundamenta mathematicae, vol. 3, pp. 133-181, 1922, doi: 10.4064/fm-3-1-133-181. [ Links ]

[2] V. Berinde, Iterative approximation of fixed points, vol. 1912. Berlin: Springer, 2007, doi: 10.1007/978-3-540-72234-2. [ Links ]

[3] A. Granas and J. Dugundji, Fixed point theory. New York, NY: Springer, 2010,doi: 10.1007/978-0-387-21593-8. [ Links ]

[4] P. Hitzler and A. K. Seda, “The fixed-point theorems of priess-crampe and ribenboim in logic programming”, in Valuation theory and its applications, vol. 1, F.- V. Kuhlmann, S. Kuhlmann, and M. Marshall, Eds. Providence, RI: American Mathematical Society, 2002, pp. 219-235, doi: 10.1090/fic/032. [ Links ]

[5] B. Hughes, “Trees and ultrametric spaces: a categorical equivalence”, Advances in mathematics, vol. 189, no. 1, pp. 148-191, Dec. 2004, doi: 10.1016/j.aim.2003.11.008. [ Links ]

[6] M. A. Khamsi and W. A. Kirk, An Introduction to metric spaces and fixed point theory. New York, NY: John Wiley and sons, 2001, doi: 10.1002/9781118033074. [ Links ]

[7] A. Y. Khrennikov, S. V. Kozyrev, and W. A. Zúñiga-Galindo, Ultrametric pseudodifferential equations and applications, vol. 168. Cambridge: Cambridge University Press, 2018, doi: 10.1017/9781316986707. [ Links ]

[8] W. A. Kirk and N. Shahzad, “Some fixed point results in ultrametric spaces”, Topology and its applications, vol. 159, no. 15, pp. 3327-3334, Sep. 2012, doi: 10.1016/j.topol.2012.07.016. [ Links ]

[9] W. A. Kirk andN. Shahzad , Fixed point theory in distance spaces. Cham: Springer, 2014, doi: 10.1007/978-3-319-10927-5. [ Links ]

[10] C. Perez-Garcia and W. H. Schikhof, Locally convex spaces over non- archimedean valued field, vol. 119. Cambridge: Cambridge University Press , 2010, doi: 10.1017/CBO9780511729959. [ Links ]

[11] C. Petalas and T. Vidalis, “A fixed point theorem in non-archimedean vector spaces”, Proceedings of the American Mathematical Society, vol. 118, no. 3, pp. 819-821, 1993, doi: 10.1090/S0002-9939-1993-1132421-2. [ Links ]

[12] S. Priess-Crampe and P. Ribenboim, “Logic programming and ultrametric spaces”, Rendiconti di matematica e delle sue applicazioni, vol. 19, no. 2, pp. 155-176, 1999. [On line]. Available: https://bit.ly/2Yh0RC7 Links ]

[13] S. Priess-Crampe and P. Ribenboim , “Ultrametric spaces and logic programming”, The journal of logic programming, vol. 42, no. 2, pp. 59-70, Feb. 2000, doi: 10.1016/s0743-1066(99)00002-3. [ Links ]

[14] S. Priess-Crampe and P. Ribenboim , “Ultrametric dynamics”, Illinois journal of mathematics, vol. 55, no. 1, pp. 287-303, 2011. [On line]. Available: https://bit.ly/2VNH7EuLinks ]

[15] A. C. M. van Rooij, Non-archimedean functional analysis. New York, NY: M. Dekker, 1978. [ Links ]

Received: June 30, 2019; Accepted: August 30, 2019

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License