International Journal of Applied Engineering Research, Dindigul
  • Year: 2010
  • Volume: 1
  • Issue: 3

Fixed Points theorem in Fuzzy Metric Space for weakly Compatible Maps satisfying Integral type Inequality

  • Author:
  • Manish Kumar Mishra1,, Priyanka Sharma2, D.B. Ojha3
  • Total Page Count: 9
  • Page Number: 315 to 323

1Research Scholar, Department of Mathematics, Singhania University

2Research Scholar, Department of Mathematics, Mewar University

3Department of mathematics, R.K.G.I.T. U.P.T.U Delhi, Meerut road, Ghaziabad

*Email: mkm2781@rediffmail.com

Abstract

In this paper, we prove some fixed point theorems for weakly compatible maps in fuzzy metric space satisfying integral type inequality but without assuming the completeness of the space or continuity of the mappings involved.We extend this concept to fuzzy metric space and establish the existence of common fixed points for a pair of self mappings. The result obtained in the fuzzy metric space by using the notion of noncomapatible maps or the property (E.A) are very interesting. we prove common fixed point theorems for weakly compatible maps in fuzzy metric space by using the concept of (E.A) property, however, without assuming either the completeness of the space or continuity of the mappings involved. We also find an affirmative answer in fuzzy metric space to the problem of Rhoadese.

Keywords

Fuzzy metric space, non compatible maps, weakly compatible maps, common fixed point, E.A property