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Extensions of best approximation and coincidence theorems. (English) Zbl 0903.41020

Using the fixed point theory developed by the author [J. Korean Math. Soc. 29, No. 1, 191-208 (1992; Zbl 0758.47048)], in the present paper there are derived best approximation and coincidence theorems for a large class of multifunctions. These results include and unify many known theorems of different types, including classical, as well as recent results of other authors. A list of fifty previous theorems that are generalized in the paper is explicitly given.

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
55M20 Fixed points and coincidences in algebraic topology

Citations:

Zbl 0758.47048
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