A Common Fixed Point Theorem for R-Weakly Commuting Maps Satisfying Property (E.A.) in Fuzzy Metric Spaces Using Implicit Relation

Full Text (PDF, 253KB), PP.44-50

Views: 0 Downloads: 0

Author(s)

Saurabh Manro 1,*

1. School of Mathematics and Computer Applications, Thapar University Patiala (Punjab)

* Corresponding author.

DOI: https://doi.org/10.5815/ijmecs.2012.11.04

Received: 12 Aug. 2012 / Revised: 4 Sep. 2012 / Accepted: 2 Oct. 2012 / Published: 8 Nov. 2012

Index Terms

Fuzzy metric space, R-weakly commuting mappings, Property (E.A.), Common (E.A) property, Implicit relation

Abstract

The purpose of this paper is to prove a common fixed theorem for R-weakly commuting mappings via an implicit relation in fuzzy metric space. While proving our result, we utilize the idea of property (E.A.) due to Aamri and El. Moutawakil [1] together with common (E.A.) property due to Liu, Wu and Li [2].

Cite This Paper

Saurabh Manro, "A Common Fixed Point Theorem for R-Weakly Commuting Maps Satisfying Property (E.A.) in Fuzzy Metric Spaces Using Implicit Relation", International Journal of Modern Education and Computer Science(IJMECS), vol.4, no.11, pp.44-50, 2012. DOI:10.5815/ijmecs.2012.11.04

Reference

[1]M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188.
[2]W. Lui, J. Wu and Z. Li, Common fixed points of single-valued and multivalued maps, Int. J. Math. Math. Sci, 19 (2005), 3045-3055.
[3]G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986), 771-779.
[4]G. Jungck and B.E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227-238.
[5]J. X. Fang and Y. Gao, Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Analysis, 70 (1) (2009), 184-193.
[6]M. Imdad, M. Tanveer and M. Hasan, Some common fixed point theorems in Menger PM-spaces, Fixed Point Theory and Applications, Volume 2010, Article ID 819269, 14 pages.
[7]S. Kumar and B. Fisher, A common fixed point theorem in fuzzy metric space using property (E. A.) and implicit relation, Thai J. Math., 8 (3) (2010), 439-446.
[8]D. Mihet, Fixed point theorems in fuzzy metric spaces using property E.A., Nonlinear Analysis, 73 (7) (2010), 2184-2188.
[9]S.S. Bhatia, S. Manro and S. Kumar, Fixed point theorem for weakly compatible maps using E.A. Property in Fuzzy metric spaces satisfying contractive condition of Integral type, Int. J. Contemp. Math. Sciences, 5 (51)(2010), 2523 – 2528.
[10]S. Manro, A Common Fixed Point Theorem for Weakly Compatible Maps Satisfying Property (E.A.) in Fuzzy Metric Spaces using Strict Contractive Condition. ARPN Journal of Science and Technology, 2(4) ( 2012), 367-370.
[11]S. Manro, S.S. Bhatia and S. Kumar, Common fixed point theorems in fuzzy metric spaces, Annals of Fuzzy Mathematics and Informatics, 3(1)(2012), 151- 158.
[12]K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. (USA), 28 (1942), 535-537.
[13]I. Kramosil and J. Michalek, Fuzzy metric and statistical spaces, Kybernetica, 11(1975), 336–344.