Fixed point theorems for cyclic mappings in quasi-partial b-metric spaces
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Authors
Xiaoming Fan
- School of Mathematical Sciences, Harbin Normal University, Harbin, 150025, P. R. China.
Abstract
In this paper, we introduce the concepts of qpb-cyclic-Banach contraction mapping, qpb-cyclic-Kannan
mapping and qpb-cyclic \(\beta\)-quasi-contraction mapping and establish the existence and uniqueness of fixed
point theorems for these mappings in quasi-partial b-metric spaces. Some examples are presented to validate
our results.
Share and Cite
ISRP Style
Xiaoming Fan, Fixed point theorems for cyclic mappings in quasi-partial b-metric spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2175--2189
AMA Style
Fan Xiaoming, Fixed point theorems for cyclic mappings in quasi-partial b-metric spaces. J. Nonlinear Sci. Appl. (2016); 9(5):2175--2189
Chicago/Turabian Style
Fan, Xiaoming. "Fixed point theorems for cyclic mappings in quasi-partial b-metric spaces." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2175--2189
Keywords
- Quasi-partial b-metric space
- fixed point theorems
- qpb-cyclic-Banach contraction mapping
- qpb-cyclic-Kannan mapping
- qpb-cyclic \(\beta\)-quasi-contraction mapping
MSC
References
-
[1]
A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 10 pages.
-
[2]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181.
-
[3]
M. A. Bukatin, S. Y. Shorina, Partial metrics and co continuous valuations, in Foundations of Software Science and Computation Structure, (Lisbon, 1998) Lecture Notes in Comput. Sci., 1378, Springer, Berlin, (1998), 125- 139.
-
[4]
L. B. Ćirić, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267-273.
-
[5]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11.
-
[6]
A. Gupta, P. Gautam, Quasi-partial b-metric spaces and some related fixed point theorems, Fixed Point Theory Appl., 2015 (2015), 12 pages.
-
[7]
P. Hitzler, A. K. Seda, Dislocated topologies, J. Electr. Eng., 51 (2000), 3-7.
-
[8]
N. Hussain, J. R. Roshan, V. Parvaneh, M. Abbas , Common fixed point results for weak contractive mappings in ordered b-dislocated metric spaces with applications, J. Inequal. Appl., 2013 (2013), 21 pages.
-
[9]
R. Kannan, Some results on fixed points - II, Amer. Math. Monthly, 76 (1969), 405-408.
-
[10]
E. Karapinar, I. M. Erhan, A. Öztürk, Fixed point theorems on quasi-partial metric spaces, Math. Comput. Modelling, 57 (2013), 2442-2448.
-
[11]
E. Karapinar, I. M. Erhan, Best proximity point on different type contractions, Appl. Math. Inf. Sci., 5 (2011), 558-569.
-
[12]
W. A. Kirk, P. S. Srinivasan, P. Veeramani , Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), 79-89.
-
[13]
C. Klin-eam, C. Suanoom, Dislocated quasi-b-metric spaces and fixed point theorems for cyclic contractions, Fixed Point Theory Appl., 2015 (2015), 12 pages.
-
[14]
S. G. Matthews, Partial Metric Topology, Research Report 212, Department of Computer Science, University of Warwick (1992)
-
[15]
S. G. Matthews, Partial metric topology, General Topology and its Applications, Ann. New York Acad. Sci., 728 (1992), 183-197.
-
[16]
A. Roldán-López-de-Hierro, E. Karapinar, M. De la Sen, Coincidence point theorems in quasi-metric spaces without assuming the mixed monotone property and consequences in G-metric spaces, Fixed Point Theory Appl., 2014 (2014), 29 pages.
-
[17]
S. Shukla , Partial b-metric spaces and fixed point theorems, Mediterr. J. Math., 11 (2014), 703-711.
-
[18]
C. Zhu, C. Chen, X. Zhang, Some results in quasi-b-metric-like spaces, J. Inequal. Appl., 2014 (2014), 8 pages.
-
[19]
W. A. Wilson, On quasi-metric spaces, Amer. J. Math., 53 (1931), 675-684.