Coincidence point theorems in certain topological spaces

• Autorzy: Jong Soo Jung , Yeol Je Cho , Shin Min Kang , Yong Kab Choi , Byung Soo Lee
• 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.

Słowa kluczowe

EN

Generating spaces of quasi-metric family; coincidence points; fixed points; fuzzy metric spaces; probabilistic metric spaces

Kategorie tematyczne

• 54C60: Set-valued maps
• 54H25: Fixed-point and coincidence theorems
• 54A40: Fuzzy topology

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1999
• Tom: 19
• Numer: 1-2
• Strony: 85-101

Daty

wydano

1999

otrzymano

1998-02-17

Twórcy

autor

Jong Soo Jung

• Department of Mathematics, Dong-A University, Pusan 604-714, Korea

autor

Yeol Je Cho

• Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea

autor

Shin Min Kang

• Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea

autor

Yong Kab Choi

• Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea

autor

Byung Soo Lee

• 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.
• [2] H. Brézis and F.F. Browder, A general principle on ordered sets in nonlinear functional analysis, Advance in Math. 21 (1976), 355-364.
• [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.
• [7] D. Downing and W.A. Kirk, A generalization of Caristi's theorem with applications to nonlinear mapping theory, Pacific J. Math. 69 (1977), 339-346.
• [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.
• [16] S. Park, On extensions of Caristi-Kirk fixed point theorem, J. Korean Math. Soc. 19 (1983), 143-151.
• [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.