Remarks on Common Fixed Point Results in \(C^*\)-Algebra-Valued Metric Spaces

Lakshmi Kanta Dey, Tanusri Senapati

Abstract


In this short note, we study the article of Xin et al. [J. Nonlinear Sci. Appl., (9) 2016] and unexpectedly notice that the common fixed point results of this article do not produce any new result in literature. In fact the main results of this article coincide with some consequences of previous published results.


Keywords


\(C^*\)-algebra; Common fixed point

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References


Z. Kadelburg, S. Radenovic, Fixed point results in C-algebra-valued metric spaces are direct consequences of their standard metric counterparts. Fixed point Theory Appl., 53, 2016.

S. Radenovic, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5 (1), 2011, 38-50.

M. Abbas, G. Jungck, Common xed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341, 2008, 416-420.

Z.H. Ma, L.N. Jiang, H. Sun, C-algebra-valued metric spaces and related xed point theorems, Fixed Point Theory Appl. 206, 2014.

H.H. Alsulami, R.P. Agarwal, E. Karapinar, F. Khojasteh, A short note on C-valued contraction mappings, J. Inequalities Appl. 50, 2016.

L.G. Huang, X. Zhang, Cone metric spaces and xed point theorems for contractive map-pings, J. Mat. Anal. Appl. 332(2), 2007, 1468-1476.

Q. Xin, L. Jiang, Z. Ma, Common xed point theorems in C-algebra-valued metric spaces. J. Nonlinear Sci. Appl., 9, 2016.




DOI: http://dx.doi.org/10.26713%2Fjims.v10i1-2.618

eISSN 0975-5748; pISSN 0974-875X