• A FIXED POINT THEOREM FOR SET-VALUED MAPPING IN NORMED SPACE*

Xiaolan Liu*, Feng Zhou

Abstract


We present a fixed point theorem for set-valued theorem in completed normed space. In this paper, we introduce the notion of the distance between two sets, i. e, Horsdorff-distance, and provide an proof for the fixed point theorem which says that if a linear mapping defined on a open ball of a completed normed space X satisfies some conditions without compactness assumptions on the domain and range sets, then it has a fixed point on the same open ball.

Key words: A fixed point theorem, normed space, linear operator, Horsdorff-distance.

AMS subject classifications: 90C25, 90C33.

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