IJPAM: Volume 110, No. 4 (2016)

Title

SOME FIXED POINT THEOREMS IN $b$-METRIC SPACES

Authors

Siqi Xie$^1$, Yamin Wang$^2$, Linan Zhong$^3$
$^{1,2,3}$Department of Mathematics
Yanbian University
Yanji, 133000, P.R. CHINA

Abstract

The aim of this paper is to establish the structure of $b$-metric spaces, as a generalization of 2-metric spaces. Some fixed point results for generalized contractive-type mappings in the $b$-metric spaces are presented. An example is presented to support our results.

History

Received: June 8, 2016
Revised: December 1, 2016
Published: November 9, 2016

AMS Classification, Key Words

AMS Subject Classification: 54H25, 47H10
Key Words and Phrases: $b$-metric spaces, common fixed point, generalized contractive-type mapping

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 application aux$\acute{e}$quations int $\acute{e}$grales, Fundam. Math., 3 (1922), 133-181.

2
N. Hussain, A.R. Khan, R.P. Agarwal, Krasnosel$\acute{s}$kii and Ky Fan type fixed point theorems in ordered Banach spaces, J. Nonlinear Convex A., 11, No. 3, (2010) 475-489.

3
R.P. Agarwal, M.A. El-Gebeily, D. O'Rgan, Generalized contractions in partially ordered metric spaces, Appl. Anal., 87 (2008), 109-116.

4
B.H. Jiang, S.Y. Xu, L. Shi, Fixed point theorems for a class of $\alpha$-admissible contractions and applications to boundary value problem, Abstr. Appl. Anal. (2014), 1-9.

5
S. Chauhan, M. Imdad, C. Vetro, Unified metrical common fixed point theorems in 2-metric spaces via an implicit relation, J. Funct. Space. Appl. (2013), 1-11.

6
N.V. Dung, N.T. Hieu, et al, Remarks on the fixed point problem of 2-metric spaces, Fixed Point Theory A. (2013), 1-6.

7
A. Aliouche, C. Simpson, Fixed points and lines in 2-metric spaces, Adv. Math., 229 (2012), 668-690.

8
T. Marin, S. Romaguera, P. Tirado, Weakly contractive multivalued maps and $w$-distances on complete quasi-metric spaces, Fixed Point Theory A (2011), 1-900.

9
F. Khojasteh, Z. Goodarzi, A. Razani, Erratum to ''Some fixed point theorems of integral type contraction in cone metric space'', Fixed Point Theory A (2011), 1-2.

10
D. Dukic, Z. Kadelburg, S. Radenovi, Fixed points of Geraghty-Type mappings in various generalized metric spaces, Abstr. Appl. Anal. (2011), 1-13.

11
M. Jovanovi, Z. Kadelburg, S. Radenovic, Common fixed point results in metric-type spaces, Fixed Point Theory Appl. (2010), 1-15.

12
M. A. Khamsi, N. Hussain, $KKM$ mappings in metric type spaces, Nonlinear Anal., 73 (2010), 123-129.

13
W. Shatanawi, Fixed point theory for contractive mapping satisfying $\phi$-maps in $G$-metric spaces, Fixed Point Theory Appl. (2010), 1-9.

14
M. Imdad, J. Ali, A general fixed point theorem in fuzzy metric spaces via an implicit function, J. Appl. Math. Inform., 26 (2008), 591-603.

15
M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in $b$-metric spaces, Cent. Eur. J. Math., 8 (2010), 367-377.

16
A. Aghajani, M. Abbas, J.R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered $b$-metric spaces, Math. Slovaca., 64 (2014), 941-960.

17
I.A. Bakhtin, The contraction principle in quasi-metric spaces, Functional Analysis, 30 (1989), 26-37.

18
S.L. Singh, B. Prasad, Some coincidence theorems and stability of iterative procedures, Comput. Math. Appl., 55 (2008), 2512-2520.

19
M. Boriceanu, Strict fixed point theorems for multivalued operators in $b$-metric spaces, Int. J. Mod. Math., 4 (2009), 285-301.

20
J.R. Roshan, V. Parvaneh, et al, Common fixed points of almost generalized $(\psi,\varphi)_s$-contractive mappings in ordered $b$-metric spaces, Fixed Point Theory Appl. (2013), 1-9.

21
W. Shatanawi, A. Pitea, R. Lazovic, Contraction conditions using comparison functions on $b$-metric spaces, Fixed Point Theory Appl. (2014), 1-11.

How to Cite?

DOI: 10.12732/ijpam.v110i4.1 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: 2016
Volume: 110
Issue: 4
Pages: 571 - 580


$b$-METRIC SPACES%22&as_occt=any&as_epq=&as_oq=&as_eq=&as_publication=&as_ylo=&as_yhi=&as_sdtAAP=1&as_sdtp=1" title="Click to search Google Scholar for this entry" rel="nofollow">Google Scholar; DOI (International DOI Foundation); WorldCAT.

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