Some new results in the framework of Sb-metric spaces
Authors: Saleem N., Ansari A.H., Pavlović M., Radenović S.
Keywords: common fixed point; C- class function; refinement inequality; Sb-metric space
Abstract:
In this paper, we consider Sb-metric space as a generalization of metric space. Also we obtained some common fixed point results using C-class function with refinement inequality in Sb-metric spaces. Further, we present one example, which shows that obtained results are proper generalization of the results in literature.
References:
[1] Abbas, M., Nazir, T., Radenović, S. (2011) Common fixed points of four maps in partially ordered metric spaces. Applied Mathematics Letters, 24(9): 1520-1526
[2] Ansari, A.H. (2014) Note on ‘φ -y-contractive type mappings and related fixed point. u: The 2nd Regional Conference on Mathematics And Applications, PNU, 377-380
[3] Bakhtin, I.A. (1989) The contraction principle in quasi metric spaces. Funct. Anal. Gos. Ped. Inst. Unianowsk, 30, 26-37
[4] Banach, S. (1922) Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta Mathematicae, 3: 133-181
[5] Czerwik, S. (1993) Contraction Mappings in b-metric spaces. Acta Mathematica et Informatica Universitatis Ostraviensis, 1, 5-11
[6] Dung, N. (2013) On coupled common fixed points for mixed weakly monotone maps in partially ordered S-metric spaces. Fixed Point Theory and Applications, 2013(1): 48
[7] Jungck, G. (1986) Compatible mappings and common fixed points. International Journal of Mathematics and Mathematical Sciences, 9(4): 771-779
[8] Khan, M.S., Swaleh, M., Sessa, S. (1984) Fixed point theorems by altering distances between the points. Bulletin of the Australian Mathematical Society, 30(01): 1
[9] Kishore, G., Rao, K., Panthi, D., Srinuvasa, R.B., Satyanaraya, S. (2016) Some applications via fixed point results in partially ordered S b. Fixed Point Theory and Applications, 2017(1):
[10] Rahimi, H., Soleimani, R.G. (2012) Some fixed point results in metric type space. J. Basic Appl. Sci. Res, 2(9): 3901-3908
[11] Rahimi, H., Abbas, M., Rad, G. (2015) Common fixed point results for four mappings on ordered vector metric spaces. Filomat, 29(4): 865-878
[12] Rohen, Y., Dosenovic, T., Radenovic, S. (2017) A note on the paper ‘A fixed point theorems in Sb-metric spaces’. Filomat, 31(11): 3335-3346
[13] Roshan, J.R., Shobkolaei, N., Sedghi, S., Abbas, M. (2014) Common fixed point of four maps in b-metric spaces. Hacett. J. Math. Stat., 43 (4): 613-624
[14] Sedghi, S., Altun, I., Shobe, N., Salahshour, M.A. (2014) Some Properties of S-metric Spaces and Fixed Point Results. Kyungpook mathematical journal, 54(1): 113-122