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Xu, Shaoyuan, Cheng, Suyu, Radenović, Stojan. (1397). Some notes on ``Common fixed point of two $R$-weakly commuting mappings in $b$-metric spaces". هنرهای کاربردی, 9(2), 161-167. doi: 10.22075/ijnaa.2018.3060.1495
Shaoyuan Xu; Suyu Cheng; Stojan Radenović. "Some notes on ``Common fixed point of two $R$-weakly commuting mappings in $b$-metric spaces"". هنرهای کاربردی, 9, 2, 1397, 161-167. doi: 10.22075/ijnaa.2018.3060.1495
Xu, Shaoyuan, Cheng, Suyu, Radenović, Stojan. (1397). 'Some notes on ``Common fixed point of two $R$-weakly commuting mappings in $b$-metric spaces"', هنرهای کاربردی, 9(2), pp. 161-167. doi: 10.22075/ijnaa.2018.3060.1495
Xu, Shaoyuan, Cheng, Suyu, Radenović, Stojan. Some notes on ``Common fixed point of two $R$-weakly commuting mappings in $b$-metric spaces". هنرهای کاربردی, 1397; 9(2): 161-167. doi: 10.22075/ijnaa.2018.3060.1495

Some notes on ``Common fixed point of two $R$-weakly commuting mappings in $b$-metric spaces"

International Journal of Nonlinear Analysis and Applications
مقاله 13، دوره 9، شماره 2، اسفند 2018، صفحه 161-167    اصل مقاله (345.4 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2018.3060.1495
نویسندگان
Shaoyuan Xu* 1؛ Suyu Cheng2؛ Stojan Radenović3
1School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China
2Library, Hanshan Normal University, Chaozhou, 521041, China
3University of Belgrade, Faculty of Mechanical Engineering, Beograd, Serbia
تاریخ دریافت: 01 بهمن 1395،  تاریخ بازنگری: 03 آبان 1396،  تاریخ پذیرش: 27 بهمن 1396 
چکیده
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.
کلیدواژه‌ها
$b$-metric spaces؛ $R$-weakly commuting mappings؛ the continuity concerning the $b$-metric؛ common fixed points
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