A note on a fixed point theorem on topological cylinders

作者：Feltrin Guglielmo^*

来源：Annali di Matematica Pura ed Applicata, 2017, 196(4): 1441-1458.

DOI：10.1007/s10231-016-0623-2

• Fixed point theorems
• Fixed point index
• Brouwer fixed point theorem
• Schauder fixed point theorem
• Krasnosel'skil fixed point theorem in cones

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. 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, as Brouwer, Schauder and Krasnosel'skil ones.

• 出版日期2017-8