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1999 | 19 | 1-2 | 85-101
Tytuł artykułu

Coincidence point theorems in certain topological spaces

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we establish some new versions of coincidence point theorems for single-valued and multi-valued mappings in F-type topological space. As applications, we utilize our main theorems to prove coincidence point theorems and fixed point theorems for single-valued and multi-valued mappings in fuzzy metric spaces and probabilistic metric spaces.
Twórcy
  • Department of Mathematics, Dong-A University, Pusan 604-714, Korea
autor
  • Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea
  • Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea
  • Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea
  • Department of Mathematics, Kyungsung University, Pusan 608-736, Korea
Bibliografia
  • [1] J.S. Bae, E.W. Cho and S.H. Yeom, A generalization of the Caristi-Kirk fixed point theorem and its applications to mapping theorems, J. Korean Math. Soc. 31 (1994), 29-48.
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  • [3] J. Caristi, Fixed point theorems for mapping satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 (1976), 241-251.
  • [4] S.S. Chang and Q. Luo, Set-valued Caristi's fixed point theorem and Ekeland's variational principle, Appl. Math. and Mech. 10 (1989), 119-121.
  • [5] S.S. Chang, Y.Q. Chen and J.L. Guo, Ekeland's variational principle and Caristi's fixed point theorem in probabilistic metric spaces, Acta Math. Appl. 7 (1991), 217-228.
  • [6] S.S. Chang, Y.J. Cho, B.S. Lee, J.S. Jung and S.M. Kang, Coincidence point theorems and minimization theorems in fuzzy metric spaces, Fuzzy Sets and Systems 88 (1997), 119-127.
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  • [8] J.X. Fang, On the generalizations of Ekeland's variational principle and Caristi's fixed point theorem, The 6-th National Conference on the Fixed Point Theory, Variational Inequalities and Probabilistic Metric Spaces Theory, 1993, Qingdao, China.
  • [9] J.X. Fang, The variational principle and fixed point theorems in certain topological spaces, J. Math. Anal. Appl. 202 (1996), 398-412.
  • [10] P.J. He, The variational principle in fuzzy metric spaces and its applications, Fuzzy Sets and Systems 45 (1992), 389-394.
  • [11] J.S. Jung, Y.J. Cho and J.K. Kim, Minimization theorems for fixed point theorems in fuzzy metric spaces and applications, Fuzzy Sets and Systems 61 (1994), 199-207.
  • [12] J.S. Jung, Y.J. Cho, S.M. Kang and S.S. Chang, Coincidence theorems for set-valued mappings and Ekelands's variational principle in fuzzy metric spaces, Fuzzy Sets and Systems 79 (1996), 239-250.
  • [13] J.S. Jung, Y.J. Cho, S.M. Kang, B.S. Lee and Y.K. Choi, Coincidence point theorems in generating spaces of quasi-metric family, to appear in Fuzzy Sets and Systems.
  • [14] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems 12 (1984), 215-229.
  • [15] N. Mizoguchi and W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989), 177-188.
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  • [17] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 313-334.
  • [18] J. Siegel, A new proof of Caristi's fixed point theorem, Proc. Amer. Math. Soc. 66 (1977), 54-56.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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