IJPAM: Volume 113, No. 1 (2017)

Title

COMMON FIXED POINT THEOREM FOR
MULTI-VALUED MAPPINGS ON B-METRIC SPACES

Authors

Chanakan Jinakul$^1$, Araya Wiwatwanich$^2$, Annop Kaewkhao$^3$
$^{1,2,3}$Department of Mathematics
Faculty of Science
Burapha University
Chonburi Province 20131, THAILAND
Centre of Excellence in Mathematics
PERDO, CHE, Thailand

Abstract

In this paper, we prove a common fixed point theorem for multi-valued mappings in complete b-metric spaces. The conditions for existence of a common fixed point had been investigated. The main result can be regarded as a generalization of previous results in complete metric space.

History

Received: January 20, 2017
Revised: February 21, 2017
Published: February 28, 2017

AMS Classification, Key Words

AMS Subject Classification: 47H10, 54H25
Key Words and Phrases: common fixed point, multi-valued mapping, b-metric space

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fundamenta Mathematicae, 3 (1922), 133-181.

2
R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76.

3
R. Kannan, Some results on fixed points-II, Amer. Math. Monthly., 76, No.4 (1969), 405-408, doi: https://doi.org/10.2307/2316437.

4
W.A. Kirk, P.S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4, No.1 (2003), 79-89.

5
S.B. Nadler, Multivalued contraction mappings, Pacific Journal of Mathematics, 30, No. 2 (1969), 475-488.

6
P. Srivastava, V.K. Gupta, A note on common fixed points, Yokohama Math.J., 19 (1971), 91-95.

7
J. Jungck, Conmuting mappings and fixed points, Amer. Math. Monthly., 83, No.4 (1976), 63-261, doi: https://doi.org/10.2307/2318216.

8
L.J. Lin, S.Y. Wang, Common Fixed Point Theorems for a Finite Family of Discontinuous and Noncommutative Maps, Fixed Point Theory and Applications, (2011), 9 pages, doi: https://doi.org/10.1155/2011/847170.

9
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav., 1 (1993), 5-11.

10
H. Aydi, M.F. Bota, E. Karapinar, S. Mitrovic, A fixed point theorem for set-valued quasicontractions in b-metric spaces, Fixed Point Theory Appl., (2012), 8 pages, doi: https://doi.org/10.1186/1687-1812-2012-88.

11
M. Bota, Dynamical aspects in the theory of multivalued operators PhD thesis, (n.d).

12
S. Reich, Some problems and results in fixed point theory, Contemporary Mathematics, 21 (1983), 179-187, doi: https://doi.org/10.1090/conm/021.

13
N. Mioguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, Journal of Mathematical Analytic and Applications, 141 (1989), 172-188, doi: https://doi.org/10.1016/0022-247X(89)90214-X.

14
S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Semin. Mat. Fis. Univ. Modena., 46, No.3 (1998), 263-276.

15
M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math., 8 (2010), 367-377, doi: https://doi.org/10.2478/s11533-010-0009-4.

16
S. Czerwik, K. Dlutek, S.L. Singh, Round-off stability of iteration procedures for operators in b-metric spaces, J. Natur. Phys. Sci., 11 (1997), 87-94.

How to Cite?

DOI: 10.12732/ijpam.v113i1.15 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 1
Pages: 167 - 179


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).