Article Sidebar

Submitted
June 18, 2020
Accepted
September 3, 2020
Published
November 5, 2020
Download
PDF
Statistic
Read Counter : 498 Download : 408

Downloads

Download data is not yet available.

Main Article Content

Abstract

This paper aims to introduce a new type of quasi (s,r)-contractive multi-valued operator on b-complete metric space and to extend the results for the fixed point theorems of quasi (s,r)-contractive multi-valued operator. As an application, the  existence of the solution for a type of differential equation is given.

Keywords

b-metric space quasi (s r)-contractive multi-valued operator fixed point theorem.

Article Details

Author Biographies

Ei Ei Nyein, Beijing Institute of Technology

School of Mathematics and Statistics

Aung Khaing Zaw, Beijing Institute of Technology

School of Mathematics and Statistics,

Student

How to Cite
Nyein, E. E., & Khaing Zaw, A. (2020). Quasi (s,r)-Contractive Multi-Valued Operators on b-Metric Space and Related Fixed Point Theorems. Journal of the Indonesian Mathematical Society, 26(3), 393–402. https://doi.org/10.22342/jims.26.3.941.393-402
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. S.L. Singh, S. Czerwik, K. Kr ol, A. Singh,, Coincidences and fixed points of hybrid contractions, Tamsui Oxf. J. Math. Sci., 24, (2008), 401416.
  2. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1, (1993), 5-11.
  3. S. Czerwick, Nonlinear set-valued contraction mappings in b-metric spaces, Atti del Seminario Matematico e Fisico dellUniversit‘a di Modena, 46, (1998), 263276.
  4. Ei Ei Nyein, Dianlu Tian, Aung Khaing Zaw, Quasi (s,r)-Contractive Multi-Valued Operators and Related Fixed Point Theorems, Mathematics, 2020, 8(1), 64; doi:10.3390/math8010064.
  5. M. Jleli, B. Samet, C. Vetro, F. Vetro, Fixed points for multivalued mappings in b-metric spaces, Abstract and Applied Analysis, 2015 (2015), 1-7.
  6. William Kirk, Naseer Shahzad, Fixed Point Theory in Distance Spaces, Springer, New York, (2014).
  7. Radu Miculescu, Alexandru Mihail, New fixed point theorems for set-valued contractions in b-metric spaces, arXiv:1512.03967v1 [math.CA] 12, Dec (2015).
  8. H. Aydi, M.F. Bota, E. Karapinar, S. Mitrovic, A fixed point theorem for set-valued quasicontractions in b-metric spaces, Fixed Point Theory and Applications, 2012, (2012): 88.
  9. L.B. Ciric, A generalization of Banachs contraction principle, Proc. Amer. Math. Soc., 45 (2) (1974), 267273.
  10. S.B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475488.
  11. O. Popescu, A new type of contractive multivalued operators, Bull. Sci. Math., 137, (2013), 30-44.
  12. A. Amini-Harandi, Fixed point theory for set-valued quasi-contraction maps in metric spaces, Appl. Math. Lett., 24, (2011), 1791-1794.
  13. R.H. Haghi,S. Rezapour, N. Shahzad, On fixed points of quasi-contraction type multifunctions, Appl. Math. Lett., 25, (2012), 843-846.
  14. Lingjuan Ye, Congcong Shen, weakly (s,r)-contractive multi-valued operators on b-mettric space, J.Nonlinear Sci. Appl., 11 (2018), 358-367.
  15. J.R. Roshan, V. Parvaneh, Z. Kadelburg, Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 229245.
  16. M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math., 8 (2010), 367-377.