Common fixed point theorems for two weakly compatible self-mappings in cone b -metric spaces
- PDF / 379,279 Bytes
- 16 Pages / 595 x 842 pts (A4) Page_size
- 50 Downloads / 178 Views
Common fixed point theorems for two weakly compatible self-mappings in cone $b$-metric spaces Fixed Point Theory and Applications 2013, 2013:120
doi:10.1186/1687-1812-2013-120
Lu Shi ([email protected]) Shaoyuan Xu ([email protected])
ISSN Article type
1687-1812 Research
Submission date
1 January 2013
Acceptance date
22 April 2013
Publication date
6 May 2013
Article URL
http://www.fixedpointtheoryandapplications.com/content/2013/1/120
This peer-reviewed article can be downloaded, printed and distributed freely for any purposes (see copyright notice below). For information about publishing your research in Fixed Point Theory and Applications go to http://www.fixedpointtheoryandapplications.com/authors/instructions/ For information about other SpringerOpen publications go to http://www.springeropen.com
© 2013 Shi and Xu This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
FPTA_250_edited
[05/02 11:41]
1/15
Common fixed point theorems for two weakly compatible self-mappings in cone b-metric spaces Lu Shi and Shaoyuan Xu
∗
†
School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, P.R.China
Abstract: In this paper, we establish common fixed point theorems for two weakly compatible self-mappings satisfying the contractive condition or the quasicontractive condition in the case of a quasi-contractive constant λ ∈ (0, 1/s) in cone b-metric spaces without the normal cone, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature. Keywords: common fixed point; weakly compatible self-mappings; (quasi)contractive condition; cone b-metric space
1
Introduction and preliminaries
Huang and Zhang [1] introduced the concept of a cone metric space, proved the properties of sequences on cone metric spaces and obtained various fixed point theorems for contractive mappings. The existence of a common fixed point on cone metric spaces was considered recently in [2-5]. Also, Ilic and Rakocevic [6] introduced a quasi-contraction on a cone metric space when the underlying cone was normal. Later on, Kadelburg et al. obtained a few similar results without the normality of the underlying cone, but only in the case of a quasi-contractive constant λ ∈ (0, 1/2). However, Gajic [7] proved that result is true for λ ∈ (0, 1) on a cone metric space by a new way, which answered the open question whether the result is true for λ ∈ (0, 1). Recently, Hussain and Shah [8] introduced cone b-metric spaces, as a generalization of b-metric spaces and cone metric spaces, and ∗
The research is partially supported by the Foundation of Education Ministry, Hubei Province, China (No: D20102502) † Corresponding author: Shaoyuan Xu. E-mail: [email protected] (S. Xu)
1
FPTA_250_edited
[05/02 11:41]
2/15
established som
Data Loading...
