ABSTRACT
We illustrate here how a "minimum condition" initially used in the study of fixed point theory for mappings which are not self-mappings of their domains (see [4], [6]), and then used extensively in the study of mappings satisfying local metric conditions (see, e.g., [5], [7]), also provides a criterion which guarantees the existence of fixed points for certain set-valued mappings. Our first theorem, which is for set-valued local contractions, is an analog of Proposition 1 of [5]. We then use the global version of this result to obtain a new fixed point theorem for setvalued nonexpansive pseudo-contractions.
