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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 43 | Number 1 | Year 2017 | Article Id. IJMTT-V43P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V43P509

Fixed Point Theorems for Self-Mappings in a Menger Space using Contractive Control Function under CLR / JCLR-Property


S. Rajesh
Abstract

In this paper, using contractive control function and CLR / JCLR property two fixed point theorems for self-mappings in a Menger space are mainly proved and also considered a variant of those theorems. Examples are provided in support of the theorems. 2010 Mathematics Subject Classification: 47H20, 54H25.

Keywords
Menger space, triangular norm, weakly compatible mappings, common fixed point.
References

[1] M. Abbas, I. Altun, D. Gopal, Common f ixed point theorems for non compatible mappings in fuzzy metric spaces, Bulletin of Mathematical Analysis and Applications, 2009, 1(2), 47-56.
[2] K.P.R.Sastry, G.A.Naidu, P.V.S.Prasad and S.S.A.Sastri, A Fixed Point Theorem for a sequence of self maps in a Menger Space Using a contractive control function, Int. Journal of Math. Analysis, Vol. 4, no.35, 2010, 1341-1348.
[3] B. Schweizer and A. Sklar, Statistical metric space, North-Halland Series in Probability and Applied Math 5, North-Holland, Amsterdam 1983.
[4] S. Singh and S. Jain, A fixed point theorem in Menger spaces through weakly compatibility, J. Math. Anal. Appl., 301(2005), 439-448.
[5] Sinturavarant and Kumam, Common Fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, Journal of Applied Mathematics, Vol. 2011, (2011).
[6] Sunny Chauhan, Wutiphol Sintunavarat and Poom Kumam, Common Fixed point theorems for weakly compatible mappings in fuzzy metric space using (JCLR) property, Applied Mathematics, (2012), 3, 976-982.

Citation :

S. Rajesh, "Fixed Point Theorems for Self-Mappings in a Menger Space using Contractive Control Function under CLR / JCLR-Property," International Journal of Mathematics Trends and Technology (IJMTT), vol. 43, no. 1, pp. 55-62, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V43P509

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