A Gap in the Paper "A Note on Cone Metric Fixed Point Theory and its Equivalence"

Yıl 2011, Cilt: 24 Sayı: 2, 233 - 234, 05.04.2011

Erdal Karapınar Thabet Abdeljawad

Öz

There is a gap in Theorem 2.2 of the paper of Du [1]. In this paper, we shall state the gap and repair it.  

Anahtar Kelimeler

cone metric space, tvs cone, metric space

A Gap in the Paper "A Note on Cone Metric Fixed Point

Öz

Kaynakça

• Wei-Shih, Du, “A note on cone metric fixed point theory and its equivalence”, Nonlinear Analysis, 72(5): 2259-2261 (2010).
• Huang, L. G., Zhang, X., “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 332 :1468–-1476 (2007).
• Kadelburg, Z., Radenović, S., Rakoćević, V.,: “Remarks on quasi-contraction on a cone metric space", Appl. Math. Lett., 22: 1674–1679 (2009).
• Rezapour, Sh., Hamlbarani, R., “Some notes on the paper Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 345: 719–-724(2008).
• Rezapour, Sh., Haghi, R.H., Shahzad, N., “Some Notes on fixed points of quasicontraction maps”, Appl. Math. Lett., 23: 498--502(2010).
• Rezapour, Sh., Khandani, H., Vaezpour, S.M., “Efficacy of Cones on Topological Vector Spaces and Application to Common Fixed Points of Multifunctions”, Rend. Circ. Mat. Palermo, 59 :185–197(2010).
• Karapınar, E., “Fixed Point Theorems in Cone Banach Spaces”, Fixed Point Theory Appl., 2009, Article ID 609281, 9 pages, (2009) doi:10.1155/2009/609281.