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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 4 | Issue 11 | Year 2013 | Article Id. IJMTT-V4I11P8 | DOI : https://doi.org/10.14445/22315373/IJMTT-V4I11P8

Some Common Fixed Point Theorems for Weakly Compatible Mappings in Menger Spaces


Balbir Singh , Vishal Gupta , Sanjay kumar
Abstract

In this paper, firstly we prove a common fixed point theorem for weakly compatible mappings. Secondly, we prove common fixed point theorems for weakly compatible mappings with E.A and CLR property in Menger spaces. At the end, we provide an example in support of our theorem.

Keywords
Menger space, weakly compatible mappings, t-norm of Hadzic- type, E.A. and (CLR) property.
References

[1] O. Hadzic, Some theorems on the fixed point in probabilistic metric and Random normed spaces, Bull. Unione Mat. Ital. (6), 1-B (1982), 381-391.
[2] O. Hadzic. A fixed point theorem in menger spaces. Publ.Inst. Math. Beograd, 20; 107:112, 1979.
[3] O.Hadzic and E.Pap. Fixed point theoryinprobabilisticmetric spaces. Kluwer Academic Publishers, Dordrechi, 2001.
[4] T.L., Hicks, Fixed point theory in probabilistic metric spaces, Univ. u Novom Sadu Zb. Rad. Prirod. Mat. Fak. Ser. Mat. 13 (1983), 63-72.
[5] K. Iseki, Fixed point theorems in 2-metric spaces, Math. Sem. Notes, Kobe Uni., 3 (1975), 133-136.
[6] M. Imdad and J. Ali, Jungck common fixed point theoremsin fuzzy metric spaces , Mathematical Communication 11(2006), 153-163.
[7] M. Imdad and J. Ali, Jungck's common fixed point theorem and E.A. property, Acta Mathematica Sinica 24 (2008), 87- 94.
[8] M. Imdad, B. D. Pant, S. Chauhan, Fixed point theorems in Menger spaces using the (CLRST ) property and applications,Journal of Nonlinear Analysis and Optimization: Theory and Applications (in press).
[9] G. Jungck and B.E.Rhoades, Fixed points for set valued functions without continuity, Indian Journal of pure and applied Mathematics, vol. 29, no. 3, pp. 227-238, 1998.

Citation :

Balbir Singh , Vishal Gupta , Sanjay kumar, "Some Common Fixed Point Theorems for Weakly Compatible Mappings in Menger Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 4, no. 11, pp. 324-333, 2013. Crossref, https://doi.org/10.14445/22315373/IJMTT-V4I11P8

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