Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 33 Issue 4
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- Pages.565-585
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- 1996
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
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
Abstract
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].
Keywords
- Fixed point theorem;
- fuzzy metric space;
- generating spaces of quasi-metric family;
- minimization theorems;
- probabilistic metric space