Fixed points of set-valued mappings satisfying a Banach orbital condition

Downloads

DOI:

https://doi.org/10.56754/0719-0646.2501.151

Abstract

In this note, we prove a fixed point existence theorem for set-valued functions by extending the usual Banach orbital condition concept for single valued mappings. As we show, this result applies to various types of set-valued contractions existing in the literature.

Keywords

Banach orbital condition , continuity of set-valued mappings , fixed point , Hausdorff upper semicontinuity , set-valued contraction

Mathematics Subject Classification:

47H10 , 47H04 , 54E50
  • Pages: 151–159
  • Date Published: 2023-04-24
  • Vol. 25 No. 1 (2023)

V. Berinde, “On the approximation of fixed points of weak contractive mappings”, Carpathian J. Math., vol. 19, no. 1, pp. 7–22, 2003.

V. Berinde and M. Berinde, “On a general class of multi-valued weakly Picard mappings”, J. Math. Anal. Appl., vol. 326, no. 2, pp. 772–782, 2007.

V. Berinde and M. Păcurar, “Fixed points and continuity of almost contractions”, Fixed Point Theory, vol. 9, no. 1, pp. 23–34, 2008.

S. Cho, “A fixed point theorem for a Ćirić-Berinde type mapping in orbitally complete metric spaces”, Carpathian J. Math., vol. 30, no. 1, pp. 63–70, 2014.

Lj. B. Ćirić, “A generalization of Banach’s contraction principle”, Proc. Amer. Math. Soc., vol. 45, pp. 267–273, 1974.

H. Covitz and S. B. Nadler, “Multi-valued contraction mappings in generalized metric spaces”, Israel J. Math., vol. 8, pp. 5–11, 1970.

B. Damjanović and D. Dorić, Multivalued generalizations of the Kannan fixed point theorem, Filomat, vol. 25, no. 1, pp. 125–131, 2011.

T. L. Hicks and B. E. Rhoades, “A Banach type fixed-point theorem”, Math. Japon., vol. 24, no. 3, pp. 327–330, 1979/80.

S. Kasahara, “On some generalizations of the Banach contraction theorem”, Publ. Res. Inst. Math. Sci., vol. 12, no. 2, pp. 427–437, 1976/77.

W. A. Kirk and N. Shahzad, “Normal structure and orbital fixed point conditions”, J. Math. Anal. Appl., vol. 463, no. 2, pp. 461–476, 2018.

S. B. Nadler, “Multivalued contraction mappings”, Pacific J. Math., vol. 30, no. 2, pp. 475– 488, 1969.

S. Reich, “Kannan’s fixed point theorem”, Boll. Un. Mat. Ital. (4), vol. 4, pp. 1–11, 1971.

S. Shukla, “Set-valued Preˇsić-Chatterjea type contractions”, Gazi University Journal of Science, vol. 29, no. 2, pp. 535–540, 2016.

  • Chilean Council for Scientific and Technological Research
  • FONDECYT 1200525

Downloads

Download data is not yet available.

Published

2023-04-24

How to Cite

[1]
R. Fierro and S. Pizarro, “Fixed points of set-valued mappings satisfying a Banach orbital condition”, CUBO, pp. 151–159, Apr. 2023.

Issue

Vol. 25 No. 1 (2023)

Section

Articles

License

Copyright (c) 2023 R. Fierro et. al.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.