Common fixed point theorems under strict contractive conditions in Menger probabilistic G-metric spaces
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Authors
Qiang Tu
- Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China.
Chuanxi Zhu
- Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China.
Zhaoqi Wu
- Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China.
Abstract
In this paper, a new concept of the property \(G^*-(E:A)\) in Menger PGM-spaces is introduced. Based on this,
some common fixed point theorems under strict contractive conditions for mappings satisfying the property
\(G^*-(E:A)\) in Menger PGM-spaces and the corresponding results in G-metric spaces are obtained. Finally,
an example is given to exemplify our main results.
Share and Cite
ISRP Style
Qiang Tu, Chuanxi Zhu, Zhaoqi Wu, Common fixed point theorems under strict contractive conditions in Menger probabilistic G-metric spaces, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 6, 1176--1189
AMA Style
Tu Qiang, Zhu Chuanxi, Wu Zhaoqi, Common fixed point theorems under strict contractive conditions in Menger probabilistic G-metric spaces. J. Nonlinear Sci. Appl. (2015); 8(6):1176--1189
Chicago/Turabian Style
Tu, Qiang, Zhu, Chuanxi, Wu, Zhaoqi. "Common fixed point theorems under strict contractive conditions in Menger probabilistic G-metric spaces." Journal of Nonlinear Sciences and Applications, 8, no. 6 (2015): 1176--1189
Keywords
- Common fixed point
- Menger PGM-space
- contraction
- property \(G^*-(E:A)\)
- weakly compatible mappings.
MSC
References
-
[1]
M. Aamri, D. E. Moutawakil , Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188.
-
[2]
M. Abbas, S. H. Khan, T. Nazir, Common fixed points of R-weakly commuting maps in generalized metric space, Fixed Point Theory Appl., 2011 (2011), 11 pages.
-
[3]
M. Abbas, T. Nazir, D. Dorić, Common fixed point of mappings satisfying (E.A) property in generalized metric spaces, Appl. Math. Comput., 218 (2012), 7665-7670.
-
[4]
M. Abbas, T. Nazir , S. Radenović, Some periodic point results in generalized metric spaces, Appl. Math. Comput., 217 (2010), 4094-4099.
-
[5]
M. Abbas, T. Nazir, S. Radenović, Common fixed point of power contraction mappings satisfying (E.A) property in generalized metric spaces, Appl. Math. Comput., 219 (2013), 7663-7670.
-
[6]
R. P. Agarwal, Z. Kadelburg, S. Radenović , On coupled fixed point results in asymmetric G-metric spaces, J. Inequal. Appl., 2013 (2013), 12 pages.
-
[7]
R. P. Agarwal, E. Karapinar, Remarks on some coupled fixed point theorems in G-metric spaces, Fixed point theory Appl., 2013 (2013), 33 pages.
-
[8]
J. X. Fang, Common fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Anal., 71 (2009), 1833-1843.
-
[9]
J. X. Fang, Y. Gang, Common fixed point theorems under strict contractive conditions in Menger spaces , Nonlinear Anal., 70 (2009), 184-193.
-
[10]
F. Gu , Common fixed point theorems for six mappings in generalized metric spaces, Abstr. Appl. Anal., 2012 (2012), 21 pages.
-
[11]
F. Gu, Z. Yang , Some new common fixed point results for three pairs of mappings in generalized metric spaces, Fixed Point Theory Appl., 2013 (2013), 21 pages.
-
[12]
F. Gu, Y. Yin, A new common coupled fixed point theorem in generalized metric space and applications to integral equations, Fixed Point Theory Appl., 2013 (2013), 16 pages.
-
[13]
G. Jungck , Compatible mappings and common fixed points, Internat. J. Math. Sci., 9 (1986), 771-779.
-
[14]
G. Jungck, Common fixed points for noncontinuous nonself maps on nonnumeric spaces, Far East J. Math. Sci., 4 (1996), 199-221.
-
[15]
G. Jungck, B. E. Rhoades, Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227-238.
-
[16]
Z. Liu, Y. Han, S. M. Kang, et al., Common fixed point theorems for weakly compatible mappings satisfying contractive conditions of integral type, Fixed Point Theory Appl., 2014 (2014), 16 pages.
-
[17]
K. Menger, Statistical metrics, Proc. Natl. Acad. Sci. USA., 28 (1942), 535-537.
-
[18]
S. N. Mishra , Common fixed points of compatible mappings in PM-spaces, Math. Japon., 36 (1991), 283-289.
-
[19]
Z. Mustafa, B. Sims , A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289-297.
-
[20]
R. P. Pant , Common fixed point theorems for contractive maps, J. Math. Anal. Appl., 226 (1998), 251-258.
-
[21]
R. P. Pant, R-weak commutativity and common fixed points, Soochow J. Math., 25 (1999), 37-42.
-
[22]
R. P. Pant, V. Pant , Common fixed points under strict contractive conditions , J. Math. Anal. Appl., 248 (2000), 327-332.
-
[23]
B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 313-334.
-
[24]
Y. K. Tang, S. Chang, L. Wang, Nonlinear contractive and nonlinear compatible type mappings in Menger probabilistic metric spaces , J. Inequal. Appl., 2014 (2014), 12 pages.
-
[25]
Z .Q .Wu, C. X. Zhu, X. L. Chen, Fixed point theorems and coincidence point theorems for hybrid contractions in PM-spaces, Acta Anal. Funct. Appl., 10 (2008), 339-345.
-
[26]
C. Zhou, S. Wang, L. Ćirić, et al , Generalized probabilistic metric spaces and fixed point theorems, Fixed Point Theory Appl., 2014 (2014), 15 pages.
-
[27]
C. X. Zhu, Several nonlinear operator problems in the Menger PN space, Nonlinear Anal., 65 (2006), 1281-1284.
-
[28]
C. X. Zhu, Research on some problems for nonlinear operators, Nonlinear Anal., 71 (2009), 4568-4571
-
[29]
C. X. Zhu, W. Q. Xu, Z. Q. Wu, Some fixed point theorems in generalized probabilistic metric spaces, Abstr. Appl. Anal., 2014 (2014), 8 pages.