Common fixed point results for probabilistic \(\varphi\)-contractions in generalized probabilistic metric spaces
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Authors
Jingfeng Tian
- College of Science and Technology, North China Electric Power University, Baoding, Hebei Province, 071051, P. R. China.
Ximei Hu
- China Mobile Group Hebei Co., Ltd., Baoding, Hebei Province, 071000, P. R. China.
Abstract
In this paper, we present some new fixed point and common fixed point (common coupled fixed point, common tripled
fixed point, and common quadruple fixed point) theorems of probabilistic contractions with a gauge function \(\varphi\) in generalized
probabilistic metric spaces proposed by Zhou et al. [C.-L. Zhou, S.-H. Wang, L. Ćirić, S. M. Alsulami, Fixed Point Theory Appl.,
2014 (2014), 15 pages]. Our results extend some existing results. Moreover, an example is given to illustrate our main results.
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ISRP Style
Jingfeng Tian, Ximei Hu, Common fixed point results for probabilistic \(\varphi\)-contractions in generalized probabilistic metric spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3939--3962
AMA Style
Tian Jingfeng, Hu Ximei, Common fixed point results for probabilistic \(\varphi\)-contractions in generalized probabilistic metric spaces. J. Nonlinear Sci. Appl. (2017); 10(7):3939--3962
Chicago/Turabian Style
Tian, Jingfeng, Hu, Ximei. "Common fixed point results for probabilistic \(\varphi\)-contractions in generalized probabilistic metric spaces." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3939--3962
Keywords
- Coupled fixed point
- fixed point
- metric space
- probabilistic \(\varphi\)-contractions
- gauge function.
MSC
References
-
[1]
R. P. Agarwal, E. Karapınar, Remarks on some coupled fixed point theorems in G-metric spaces, Fixed Point Theory Appl., 2013 (2013), 33 pages.
-
[2]
V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 4889–4897.
-
[3]
L. Ćirić, R. P. Agarwal, B. Samet, Mixed monotone-generalized contractions in partially ordered probabilistic metric spaces, Fixed Point Theory Appl., 2011 (2011), 13 pages.
-
[4]
J.-X. Fang, Common fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Anal., 71 (2009), 1833–1843.
-
[5]
T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379–1393.
-
[6]
D. J. Guo, V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal., 11 (1987), 623–632.
-
[7]
O. Hadžić, A fixed point theorem in Menger spaces, Publ. Inst. Math. (Beograd) (N.S.), 20 (1979), 107–112.
-
[8]
O. Hadžić, Fixed point theorems for multivalued mappings in probabilistic metric spaces, Fuzzy Sets and Systems, 88 (1997), 219–226.
-
[9]
J. Jachymski, On probabilistic \(\phi\)-contractions on Menger spaces, Nonlinear Anal., 73 (2010), 2199–2203.
-
[10]
M. Jleli, E. Karapınar, B. Samet, Further generalizations of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 9 pages.
-
[11]
M. Jleli, E. Karapınar, B. Samet, On cyclic (\(\psi,\phi\))-contractions in Kaleva-Seikkala’s type fuzzy metric spaces, J. Intell. Fuzzy Systems, 27 (2014), 2045–2053.
-
[12]
E. Karapınar, N. V. Luong, Quadruple fixed point theorems for nonlinear contractions, Comput. Math. Appl., 64 (2012), 1839–1848.
-
[13]
V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341–4349.
-
[14]
T. Luo, C.-X. Zhu, Z.-Q. Wu, Tripled common fixed point theorems under probabilistic \(\phi\)-contractive conditions in generalized Menger probabilistic metric spaces, Fixed Point Theory Appl., 2014 (2014), 17 pages.
-
[15]
K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. U. S. A., 28 (1942), 535–537.
-
[16]
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289–297.
-
[17]
V. I. Opoĭcev, Heterogeneous and combined-concave operators, (Russian) Sibirsk. Mat. Z ., 16 (1975), 781–792.
-
[18]
B. Samet, On the approximation of fixed points for a new class of generalized Berinde mappings, Carpathian J. Math., 32 (2016), 363–374.
-
[19]
B. Schweizer, A. Sklar, Probabilistic metric spaces, North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing Co., New York (1983)
-
[20]
S. Sedghi, I. Altun, N. Shobe, Coupled fixed point theorems for contractions in fuzzy metric spaces, Nonlinear Anal., 72 (2010), 1298–1304.
-
[21]
] J. Wu, Some fixed-point theorems for mixed monotone operators in partially ordered probabilistic metric spaces, Fixed Point Theory Appl., 2014 (2014), 12 pages.
-
[22]
J.-Z. Xiao, X.-H. Zhu, Y.-F. Cao, Common coupled fixed point results for probabilistic \(\phi\)-contractions in Menger spaces, Nonlinear Anal., 74 (2011), 4589–4600.
-
[23]
C.-L. Zhou, S.-H. Wang, L. Ćirić, S. M. Alsulami, Generalized probabilistic metric spaces and fixed point theorems, Fixed Point Theory Appl., 2014 (2014), 15 pages.