Some minimization theorems in generating spaces of quasi-metric family and applications

  • Jung, Jong-Soo (Dept. of Math., Dong-A University, Pusan 604-714) ;
  • Lee, Byung-Soo (Dept. of Math., Kyungsung University, Pusan 608-736) ;
  • Cho, Yeol-Je (Dept. of Math., Gyeongsang National University, Chinju 660-701)
  • Published : 1996.11.01


In 1976, Caristi [1] established a celebrated fixed point theorem in complete metric spaces, which is a very useful tool in the theory of nonlinear analysis. Since then, several generalizations of the theorem were given by a number of authors: for instances, generalizations for single-valued mappings were given by Downing and Kirk [4], Park [11] and Siegel [13], and the multi-valued versions of the theorem were obtained by Chang and Luo [3], and Mizoguchi and Takahashi [10].


Fixed point theorem;fuzzy metric space;generating spaces of quasi-metric family;minimization theorems;probabilistic metric space