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Common fixed points of multivalued functions satisfying a Boyd-Wong condition. (English) Zbl 0792.54038

Summary: Let \((X,d)\) be a complete metric space, \(C(X)\) the family of non empty closed subsets of \(X\), \(H\) the Hausdorff distance in \(C(X)\). We prove some common fixed point theorems for the sequences of multivalued functions \(T_ n: \to C(X)\) such that \[ H(T_ nx, T_ my) \leq q(x,y)\max [d(x,T_ nx), d(y,T_ m y), \textstyle{{1\over 2}}(d(x,T_ m y) + d(y,T_ n x)),d(x,y)] \] with \(q\) real nonnegative function on \(X \times X\), \(q(x,y) < 1\), satisfying a Boyd-Wong condition.

MSC:

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