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

Park, Sehie

Int. J. Math. Math. Sci. 20, No. 4, 689-698 (1997).

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.

Reviewer: R.Păltănea (Braşov)

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

Keywords:

multifunction; acyclic; convex space; upper semicontinuous; best approximation; metric projection

Citations:

Zbl 0758.47048