TY - JOUR
ID - 3522
TI - Some notes on ``Common fixed point of two $R$-weakly commuting mappings in $b$-metric spaces"
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Xu, Shaoyuan
AU - Cheng, Suyu
AU - RadenoviÄ‡, Stojan
AD - School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China
AD - Library, Hanshan Normal University, Chaozhou, 521041, China
AD - University of Belgrade, Faculty of Mechanical Engineering, Beograd, Serbia
Y1 - 2018
PY - 2018
VL - 9
IS - 2
SP - 161
EP - 167
KW - $b$-metric spaces
KW - $R$-weakly commuting mappings
KW - the continuity concerning the $b$-metric
KW - common fixed points
DO - 10.22075/ijnaa.2018.3060.1495
N2 - Very recently, Kuman et al. [P. Kumam, W. Sintunavarat, S. Sedghi, and N. Shobkolaei. Common Fixed Point of Two $R$-Weakly Commuting Mappings in $b$-Metric Spaces. Journal of Function Spaces, Volume 2015, Article ID 350840, 5 pages] obtained some interesting common fixed point results for two mappings satisfying generalized contractive condition in $b$-metric space without the assumption of the continuity of the $b$-metric, but unfortunately, there exists a gap in the proof of the main result. In this note, we point out and fill such gap by making some remarks and offering a new proof for the result. It should be mentioned that our proofs for some key assertions of the main result are new and somewhat different from the original ones. In addition, we also present a result to check the continuity of the $b$-metrics which is found effective and workable when applied to some examples.
UR - https://ijnaa.semnan.ac.ir/article_3522.html
L1 - https://ijnaa.semnan.ac.ir/article_3522_827c9ac2f28ad1c61f6bf515685d7838.pdf
ER -