Header menu link for other important links
X
Contractive modulus and common fixed point for two pairs of weakly compatible self-maps
K. Kumara Swamy,
Published in Research India Publications
2014
Volume: 10
   
Issue: 5
Pages: 737 - 744
Abstract
Let S, T and A be self-maps on a metric space (X, d) satisfying the inclusions S(X) ⊂ A(X) and T (X) ⊂ A(X) and the inequalityd(Sx, T y) ≤ φ (max{d(Ax,Ay), d(Sx, Ax), d(T y,Ay),}) for all x, y ∈ X, where φ is an upper semicontinuous contractive modulus with φ(0) = 0 and φ(t) < t whenevert > 0. Singh and Mishra (1997) proved that if any one of the subspaces S(X), T (X) and A(X) of X is complete, then S, T and A will have a common coincidence point. Further if the pairs (A, S) and (A, T) commute at their coincidence points, that is (A, S) and (A, T) are weakly compatible pairs, then S, T and A will have a unique common fixed point. The present paper extends the above result to four self-maps under weaker form of the inequality (1). It can also be shown that the weak compatibility of either of the pairs (A, S) and (A, T) is sufficient to obtain a common fixed point for the three maps. © Research India Publications.
About the journal
JournalGlobal Journal of Pure and Applied Mathematics
PublisherResearch India Publications
ISSN09731768