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

Authors

DOI:

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

Keywords:

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

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.

Author Biographies

Mohammed Babahmed, University of Moulay Ismail.

Dept.t of Mathematics, Faculty of Sciences Zitoune.

Abdelkhalek El Amrani, University Moulay Ismail.

Dept. of Mathematics, Faculty of Sciences Dhar El Mahraz,Laboratory of Mathematical Analysis and Applications (LAMA).

Samih Lazaiz, University Sidi Mohamed Ben Abdellah.

Dept.of Mathematics, Faculty of Sciences Dhar El Mahraz, Laboratory of Mathematical Analysis and Applications (LAMA).

References

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.

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

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

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.

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.

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.

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.

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.

W. A. Kirk and N. Shahzad, Fixed point theory in distance spaces. Cham: Springer, 2014, doi: 10.1007/978-3-319-10927-5.

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.

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.

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

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.

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/2VNH7Eu

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

Published

2020-04-30

How to Cite

[1]
M. Babahmed, A. El Amrani, and S. Lazaiz, “Fixed points and diametral sets for sequentially bounded mappings in orbital ultrametric spaces”, Proyecciones (Antofagasta, On line), vol. 39, no. 2, pp. 481-493, Apr. 2020.

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Section

Artículos