Common Fixed Point Theorems in Probabllistic Metric Spaces and Extension to Uniform Spaces

  • Singh, S.L. (L.M.S. Govt. Postgraduate College) ;
  • Pant, B.D. (Govt. Postgraduate College)
  • Published : 1984.08.01

Abstract

Let(X, $\Im$) be a probabilistic metric space with a t-norm. Common fixed point theorems and convergence theorems generalizing the results of Ćirić, Fisher, Sehgal, Istrătescu-Săcuiu and others are proved for three mappings P,S,T on X satisfying $F_{Pu, Pv}(qx){\geq}min\left{F_{Su,Tv}(x),F_{Pu,Su}(x),F_{Pv,Tv}(x),F_{Pu,Tv}(2x),F_{Pv,Su}(2x)\right}$ for every $u, v {\in}X$, all x>0 and some $q{\in}(0, 1)$. One of the main results is extended to uniform spaces. Mathematics Subject Classification (1980): 54H25.

Keywords

Probabilistic metric space;Menger space;generalized contraction;fixed point;uniform space