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Some generalizations of Caristi’s fixed point theorem with applications to the fixed point theory of weakly contractive set-valued maps and the minimization problem. (English) Zbl 1222.47081

Author’s abstract: We first prove some generalizations of Caristi’s fixed point theorem. Then we give some applications to the fixed point theory of weakly contractive set-valued maps and the minimization problem.

MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
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