Further fixed point results on G-metric spaces

被引:52
|
作者
Karapinar, Erdal [1 ]
Agarwal, Ravi P. [2 ,3 ]
机构
[1] Atilim Univ, Dept Math, TR-06836 Ankara, Turkey
[2] Texas A&M Univ Kingsville, Dept Math, Kingsville, TX 78363 USA
[3] King Abdulaziz Univ, Dept Math, Fac Sci, Jeddah 21589, Saudi Arabia
关键词
coupled fixed point; fixed point; ordered set; metric space; MIXED MONOTONE MAPPINGS; THEOREMS; CONTRACTION;
D O I
10.1186/1687-1812-2013-154
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Very recently, Samet et al. (Int. J. Anal. 2013: 917158, 2013) and Jleli-Samet (Fixed Point Theory Appl. 2012: 210, 2012) noticed that some fixed point theorems in the context of a G-metric space can be deduced by some well-known results in the literature in the setting of a usual (quasi) metric space. In this paper, we note that the approach of Samet et al. (Int. J. Anal. 2013: 917158, 2013) and Jleli-Samet (Fixed Point Theory Appl. 2012: 210, 2012) is inapplicable unless the contraction condition in the statement of the theorem can be reduced into two variables. For this purpose, we modify some existing results to suggest new fixed point theorems that fit with the nature of a G-metric space. The expressions in our result, the contraction condition, cannot be expressed in two variables, therefore the techniques used in (Int. J. Anal. 2013: 917158, 2013; Fixed Point Theory Appl. 2012: 210, 2012) are not applicable.
引用
收藏
页数:14
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