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Feltrin, Guglielmo

A note on a fixed point theorem on topological cylinders. (English) Zbl 1458.47030

Ann. Mat. Pura Appl. (4) 196, No. 4, 1441-1458 (2017).
Summary: We present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin [Rend. Semin. Mat., Univ. Politec. Torino 65, No. 1, 115–157 (2007; Zbl 1179.47050)]. In view of the main result, we discuss the existence of fixed points for maps defined on different types of domains and we propose alternative proofs for classical fixed point theorems such as the fixed point theorems of Brouwer, Schauder and Krasnosel’skiĭ.

Cited in 2 Documents

MSC:

47H10 Fixed-point theorems
47H11 Degree theory for nonlinear operators

Keywords:

fixed point theorems; fixed point index; Brouwer fixed point theorem; Schauder fixed point theorem; Krasnosel’skiĭ fixed point theorem in cones

Citations:

Zbl 1179.47050
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Full Text: DOI arXiv

References:

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