Coupled Fixed Point Theorem for Weakly Compatible Mappings in Menger Spaces

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References

[1] K. Menger, “Statistical Metrices,” Proceedings of the National Academy of Sciences of USA, Vol. 28, 1942, pp. 535-537. http://dx.doi.org/10.1073/pnas.28.12.535

[2] V. M. Sehgal and A. T. Bharucha-Reid, “Fixed Points of Contraction Mappings on Probabilistic Metric Spaces,” Mathematical Systems Theory, Vol. 6, No. 1-2, 1972, pp. 97-102.

http://dx.doi.org/10.1007/BF01706080

[3] B. Schweizer and A. Sklar, “Probabilistic Metric Spaces,” North Holland Series in Probability and Applied Mathematics, Vol. 5, 1983.

[4] S. N. Mishra, “Common Fixed Points of Compatible Mappings in PM-Spaces,” Mathematica Japonica, Vol. 36, 1991, pp. 283-289.

[5] G. Jungck, “Common Fixed Points for Non-Continuous Non-Self Maps on Non-Metric Spaces,” Far East Journal of Mathematical Sciences, Vol. 4, No. 2, 1996, pp. 199215.

[6] B. Singh and S. Jain, “A Fixed Point Theorem in Menger Space through Weak Compatibility,” Journal of Mathematical Analysis and Applications, Vol. 301, 2005, pp. 439-448.

http://dx.doi.org/10.1016/j.jmaa.2004.07.036

[7] J. X. Fang, “Common Fixed Point Theorems of Compatible and Weakly Compatible Maps in Menger Spaces,” Nonlinear Analysis: Theory, Methods and Applications, Vol. 71, No. 5-6, 2009, pp. 1833-1843.

[8] O. Hadzic and E. Pap, “Fixed Point Theory in Probabilistic Metric Spaces, Vol. 536 of Mathematics and Its Applications,” Kluwer Academic, Dordrecht, 2001.

[9] T. G. Bhaskar and V. Lakshmikantham, “Fixed Point Theorems in Partially Ordered Metric Spaces and Applications,” Nonlinear Analysis: Theory, Methods and Applications, Vol. 65, No. 7, 2006, pp. 1379-1393.

http://dx.doi.org/10.1016/j.na.2005.10.017

[10] V. Lakshmikantham and L. Ciric, “Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces,” Nonlinear Analysis: Theory, Methods and Applications, Vol. 70, No. 12, 2009, pp. 4341-4349.

[11] M. Abbas, M. Ali Khan and S. Redenovic, “Common Coupled Fixed Point Theorems in Cone Metric Spaces for W-Compatible Mappings,” Applied Mathematics and Computation, Vol. 217, No. 1, 2010, pp. 195-202.

http://dx.doi.org/10.1016/j.amc.2010.05.042