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IJSTR >> Volume 2- Issue 2, February 2013 Edition



International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616



Common Fixed Point Theorems For Finite Number Of Mappings Without Continuity And Compatibility In Menger Spaces

[Full Text]

 

AUTHOR(S)

Dr. Aradhana Sharma

 

KEYWORDS

 

ABSTRACT

Theorem 1 : Let A, B, S, T, I, J, L, U, P and Q be self maps on a Menger space (X, F, t) with t(a, a) ≥ a for all a  [0, 1], satisfying (1.1) P(X)  ABIL(X), Q(X)  STJU(X), (1.2) {P, STJU} or {Q, ABIL} satisfies the property (S-B), (1.3) there exists k  (0, 1) such that FPx,Qy(ku) ≥ min {FABILy,STJUx(u),FPx,STJUx(u), FQy,ABILy(u), FQy,STJUx(u), FPx,ABILy(u)} for all x, y  X and u > 0, (1.4) if one of P(X), ABIL(X), STJU(X) or Q(X) is a closed subspace of X then (i) P and STJU have a coincidence point and (ii) Q and ABIL have a coincidence point. Further if (1.5) AB = BA, AI = IA, AL = LA, BI = IB, BL = LB, IL = LI, QL = LQ, QI = IQ, QB = BQ, ST = TS, SJ = JS, SU = US, TJ = JT,TU = UT, JU = UJ, PU = UP, PJ = JP, PT = TP, (1.6) the pairs {P, STJU} and {Q, ABIL} are weakly compatible. Then A, B, S, T, I, J, L, U, P and Q have a unique common point in X.

 

REFERENCES

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