Vol. 99, No. 1, 1982

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Altman’s contractors and fixed points of multivalued mappings

K. Balakrishna Reddy and P. V. Subrahmanyam

Vol. 99 (1982), No. 1, 127–136

Let Pi : D X1 ××Xn CL(Y i) be multivalued mappings where Xi, Y i are Banach spaces and CL(Y i) is the set of all nonempty closed subsets of Y i, i = 1,,n. We prove a theorem ensuring that 𝜃i Pi(x1,,xn) for some (x1,,xn) D and deduce the fixed point theorems for multivalued mappings proved earlier by Czerwik, Nadler and Reich as corollaries. Besides, generalizations for multivalued mappings of the existence theorems proved by Altman using his theory of contractors are also obtained.

Mathematical Subject Classification 2000
Primary: 47H10
Secondary: 54H25, 58C15
Received: 3 September 1980
Published: 1 March 1982
K. Balakrishna Reddy
P. V. Subrahmanyam