Lin, Tzu-Chu Approximation theorems and fixed point theorems in cones. (English) Zbl 0653.47033 Proc. Am. Math. Soc. 102, No. 3, 502-506 (1988). A famous generalization of Schauder’s fixed point theorem due to K. Fan states that, if K is a nonempty compact convex set in a normed linear space X and f: \(K\to X\) is continuous, then \(\| x_ 0-f(x_ 0)\| =dist(f(x_ 0),K)\) for some \(x_ 0\in K\). In the present paper, parallel results are obtained for continuous condensing maps on a closed ball or annulus in cones. Some recent results of G. Li [Proc. Am. Math. Soc. 97, 277-280 (1986; Zbl 0592.47046)] are also generalized to continuous condensing maps. Reviewer: J.Appell Cited in 4 ReviewsCited in 10 Documents MSC: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces 47H10 Fixed-point theorems 41A50 Best approximation, Chebyshev systems 54H25 Fixed-point and coincidence theorems (topological aspects) Keywords:Schauder’s fixed point theorem; continuous condensing maps on a closed ball or annulus in cones Citations:Zbl 0592.47046 × Cite Format Result Cite Review PDF Full Text: DOI