Common fixed point theorems for compatible and weakly compatible maps in Menger probabilistic G-metric spaces

Volume 9, Issue 3, pp 920--932 http://dx.doi.org/10.22436/jnsa.009.03.21

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Authors

Xiaohuan Mu - 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, we prove some new common fixed point theorems for compatible and weakly compatible self-maps under \(\phi\)-contractive conditions in Menger probabilistic G-metric spaces. Our results improve and generalize many comparable results in existing literature. Finally, an example is given as an application of our main results.

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Keywords

• Menger probabilistic G-metric space
• common fixed point
• compatible maps
• weakly compatible maps.

MSC

•  47H10
•  46S10

References

• [1] R. P. Agarwal, Z. Kadelburg, S. Radenović , On coupled fixed point results in asymmetric G-metric spaces , J. Inequal. Appl., 2013 (2013), 12 pages.


• [2] R. P. Agarwal, E. Karapınar, Remarks on some coupled fixed point theorems in G-metric spaces, Fixed point theory Appl., 2013 (2013), 33 pages.


• [3] J. X. Fang, Common fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Anal., 71 (2009), 1833-1843.


• [4] J. X. Fang, Y. Gang, Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Anal., 70 (2009), 184-193.


• [5] O. Hadzic, E. Pap, Fixed point theory in probabilistic metric spaces, Kluwer Academic Publishers, Dordrecht (2001)


• [6] J. Jachymski , On probabilistic \(\varphi\)-contractions on Menger spaces, Nonlinear Anal., 73 (2010), 2199-2203.


• [7] G. Jungck , Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (1986), 771-779.


• [8] G. Jungck , Common fixed points for noncontinuous nonself maps on non metric spaces, Far East J. Math. Sci., 4 (1996), 199-215.


• [9] Z. Q. Liu, Y. Han, S. M. Kang, J. S. Ume, Common fixed point theorems for weakly compatible mappings satisfying contractive conditions of integral type, Fixed Point Theory Appl., 2014 (2014), 16 pages.


• [10] K. Menger, Statistical metrics, Proc. Natl. Acad. Sci. USA., 28 (1942), 535-537.


• [11] S. N. Mishra, Commond fixed points of compatible mappings in PM-spaces, Math. Japon, 36 (1991), 283-289.


• [12] Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289-297.


• [13] B. Schweizer, A. Sklar , Statistical metric spaces, Pacific J. Math., 10 (1960), 313-334.


• [14] 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.


• [15] J. Z. Xiao, X. H. Zhu, Y. F. Cao, Common coupled fixed point results for probabilistic \(\varphi\)-contractions in Menger spaces, Nonlinear Anal., 74 (2011), 4589-4600.


• [16] C. Zhou, S. Wang, L. Ćirić, S. M. Saud, Generalized probabilistic metric spaces and fixed point theorems, Fixed Point Theory Appl., 2014 (2014), 15 pages.


• [17] C. X. Zhu, Research on some problems for nonlinear operators, Nonlinear Anal., 71 (2009), 4568-4571.


• [18] 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.