Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2013, 1(1), 13-16
DOI: 10.12691/tjant-1-1-4
Open AccessResearch Article

On Some Well Known Fixed Point Theorems in b-Metric Spaces

Mehmet Kir1, and Hükmi Kiziltunc1

1Department of Mathematics, Faculty of Science, Ataurk Uniwersity, Erzurum-Turkey

Pub. Date: September 23, 2013
(This article belongs to the Special Issue Recent developments in the areas of mathematics)

Cite this paper:
Mehmet Kir and Hükmi Kiziltunc. On Some Well Known Fixed Point Theorems in b-Metric Spaces. Turkish Journal of Analysis and Number Theory. 2013; 1(1):13-16. doi: 10.12691/tjant-1-1-4

Abstract

In this paper, our purpose is to show that Kannan Type and Chatterjea type contractive mappings have unique fixed point in b-metric spaces. Also, we see surprisingly a way that contrary to the known (usual) metric spaces, any contraction mapping is not need to be a weak conraction mapping in b-metric spaces.

Keywords:
fixed point b-metric spaces contraction mappings

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References:

[1]  Choudhury, B. S., Unique fixed point theorem for weakly c-conytactive mappings, Kathmandu Univ. J. Sci, Eng and Tech, 5 (1),2009, 6-13.
 
[2]  Kannan, R, Some results on .xed points, Bull. Calcutta Math. Soc., 60, 1968, 71-76.
 
[3]  Chatterjea, S. K, Fixed point theorems, C.R. Acad. Bulgare Sci. 25, 1972, 727-730.
 
[4]  Czerwik, S., Contraction mappings in b-metric spaces, Acta Math inf Univ Ostraviensis. 1 (1993), 5-11.
 
[5]  Czerwik, S., Nonlinear set-valued contration mappings in b-metric spaces, Atti Sem Math Fis Univ Modena. 46(2), (1998), 263-276.
 
[6]  Boriceanu, M., Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Studia Univ Babes-Bolyai Math. LIV (3), (2009),1-14.
 
[7]  Aydi et al., A .xed point theorem for set valued quasi-contractions in b-metric spaces, Fixed Point Theory and Applications, 2012 2012:88.
 
[8]  Berinde, V., Iterative Approximation of Fixed Points, Springer, (2006).