Two type quasi-contractions on quasi metric spaces and some fixed point results
-
2066
Downloads
-
3300
Views
Authors
Hakan Şimşek
- Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey.
Ishak Altun
- Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey.
- College of Science, King Saud University, Riyadh, Saudi Arabia.
Abstract
In this paper, we introduce new concepts of quasi-contractions of type (A) and of type (B) in a quasi metric space and we
present the differences between of them. Then we present some fixed point results. In the light of the theorems it is shown that,
although the Hausdorffness condition of quasi metric space is needed for the mapping of quasi contraction of type (A), it is not
necessary to guarantee the existence of fixed point for the mapping of quasi contraction of type (B).
Share and Cite
ISRP Style
Hakan Şimşek, Ishak Altun, Two type quasi-contractions on quasi metric spaces and some fixed point results, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3777--3783
AMA Style
Şimşek Hakan, Altun Ishak, Two type quasi-contractions on quasi metric spaces and some fixed point results. J. Nonlinear Sci. Appl. (2017); 10(7):3777--3783
Chicago/Turabian Style
Şimşek, Hakan, Altun, Ishak. "Two type quasi-contractions on quasi metric spaces and some fixed point results." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3777--3783
Keywords
- Quasi metric space
- left K-Cauchy sequence
- left K-completeness
- fixed point
- quasi contraction.
MSC
References
-
[1]
E. Alemany, S. Romaguera, On right K-sequentially complete quasi-metric spaces, Acta Math. Hungar., 75 (1997), 267–278.
-
[2]
I. Altun, M. Olgun, G. Mınak, Classification of completeness of quasi metric space and some new fixed point results, Nonlinear Funct. Anal. Appl., 22 (2017), 371–384.
-
[3]
L. Ćirić, Fixed Point Theory Contraction Mapping Principle, Faculty of Mechanical Enginearing, University of Belgrade, Beograd (2003)
-
[4]
S. Cobzaş, Functional analysis in asymmetric normed spaces, Birkhuser-Springer, Basel (2013)
-
[5]
H. Dağ, G. Mınak, I. Altun, Some fixed point results for multivalued F-contractions on quasi metric spaces, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 111 (2017), 177–187.
-
[6]
H. Dağ, S. Romaguera, P. Tirado , The Banach contraction principle in quasi-metric spaces revisited, Proceeding of the Workshop on Applied Topological Structures WATS’15, (2015), 25–31.
-
[7]
J. C. Kelly, Bitopological spaces, Proc. London Math. Soc., 13 (1963), 71–89.
-
[8]
H.-P. A. Künzi, Nonsymmetric distances and their associated topologies: About the origins of basic ideas in the area of asymmetric topology, Handbook of the history of general topology (Springer), 3 (2001), 853–968.
-
[9]
I. L. Reilly, P. V. Subrahmanyam, M. K. Vamanamurthy, Cauchy sequences in quasi-pseudo-metric spaces, Monatsh. Math., 93 (1982), 127–140.
-
[10]
S. Romaguera, A. Gutiérrez , A note on Cauchy sequences in quasi-pseudometric spaces, Glasnik Mat., 21 (1986), 191– 200.
-
[11]
S. Romaguera, Left K-completeness in quasi-metric spaces, Math. Nachr., 157 (1992), 15–23.
-
[12]
M. Sarwar, M. U. Rahman, G. Ali, Some fixed point results in dislocated quasi metric (dq-metric) spaces, J. Inequal. Appl., 2014 (2014), 11 pages.