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Lou’s fixed point theorem in a space of continuous mappings. (English) Zbl 1106.47049
The purpose of this paper is twofold. First, the author gives an essentially simplified proof of a fixed point theorem of B.–D. Lou [Proc. Am. Math. Soc. 127, No. 8, 2259–2264 (1999; Zbl 0918.47046)]. Second, he shows that the proof of a similar fixed point theorem due to E. de Pascale and L. de Pascale [Proc. Am. Math. Soc. 130, No. 11, 3249–3254 (2002; Zbl 1002.47031)] does not require the use of K-normed spaces.
47H10Fixed point theorems for nonlinear operators on topological linear spaces