DOI: 10.24193/fpt-ro.2024.2.12

Authors: Jinlu Li

Abstract: In this paper, we prove some fixed point theorems in metric vector spaces, in which the continuity is not required for the considered mappings and the underlying set is not necessarily compact. We provide some concrete examples to demonstrate these theorems. We also give some counterexamples to show that every condition in the theorems is necessary for the considered mapping to have a fixed point.

Key Words and Phrases: Fixed point, metric vector space, KKM mapping, Fan-KKM theorem.

2010 Mathematics Subject Classification: 47H10, 58C30.

Published on-line: June 15th, 2024.

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