A note on cone b-metric and its related results: generalizations or equivalence?

被引:29
作者
Du, Wei-Shih [1 ]
Karapinar, Erdal [2 ]
机构
[1] Natl Kaohsiung Normal Univ, Dept Math, Kaohsiung 824, Taiwan
[2] Atilim Univ, Dept Math, TR-06836 Ankara, Turkey
关键词
TVS-cone metric space; b-metric; TVS-cone b-metric; nonlinear scalarization function; fixed point; FIXED-POINT THEOREMS; CONTRACTIVE MAPPINGS; SPACES;
D O I
10.1186/1687-1812-2013-210
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Very recently, a notion of cone b-metric was introduced as a generalization of b-metric, and some related fixed point results were obtained. In this paper, we investigate the answer to the question whether the given results generalize the existing ones or are equivalent to them.
引用
收藏
页数:7
相关论文
共 14 条
[1]  
Abdeljawad T, 2011, GAZI U J SCI, V24, P233
[2]  
Akkouchi M., 2011, ACTA U PALACKI OLOMU, V50, P5
[3]  
Aydi H, 2012, FIXED POINT THEOR-RO, V13, P337
[4]  
Bakhtin A., 1989, Funct. Anal. Unianowsk Gos. Ped. Inst, V30, P26, DOI DOI 10.1039/AP9892600037
[5]  
Chen GY, 2005, LECT NOTES ECON MATH, V541, P1, DOI 10.1007/3-540-28445-1
[6]  
Czerwik S., 1998, Atti Sem. Mat. Univ. Modena, V46, P263
[7]   On some nonlinear problems induced by an abstract maximal element principle [J].
Du, Wei-Shih .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 347 (02) :391-399
[8]   A note on cone metric fixed point theory and its equivalence [J].
Du, Wei-Shih .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (05) :2259-2261
[9]   Fixed point theorems of contractive mappings in cone b-metric spaces and applications [J].
Huang, Huaping ;
Xu, Shaoyuan .
FIXED POINT THEORY AND APPLICATIONS, 2013,
[10]   Cone metric spaces and fixed point theorems of contractive mappings [J].
Huang Long-Guang ;
Zhang Xian .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 332 (02) :1468-1476