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Abstract. Simeon Reich (1974) proved that the fixed point theorem for single-valued mappings proved by Boyd and Wong can be generalized to multivalued mappings which map points into compact sets. He then asked (1983) whether his theorem can be extended to multivalued mappings whose range consists of bounded closed sets. In this note, we provide an affirmative answer for a certain subclass of Boyd-Wong contractive mappings.

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This technical report has been reviewed and ig approved for ibljc release IAN AvR 190-1 (7b). Distribution is unlimited. A weak law of Jarge numbers is proved using a new pointwise condition on the first moments and some weak laws for weighted sums are improved upon by weakening the hypotheses. A study is made of relationships among several conditions on (X ) which appear as hypotheses in laws of large numbers. A D. BILOSS Technloal Information Oftfieo