Abstract
We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map studied. Our work generalizes severl results in approximation theory.
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Khan, A.R., Hussain, N. & Thaheem, A.B. Some generalizations of Ky Fan’s best approximation theorem. Anal. Theory Appl. 20, 189–198 (2004). https://doi.org/10.1007/BF02901443
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DOI: https://doi.org/10.1007/BF02901443
Key words
- best approximation
- fixed point
- nonexpansive multivalued map
- almost quasi-convex function
- metrizable topological vector space
- hyperconvex space