DOI: 10.24193/fpt-ro.2021.2.41

Authors: Mohamed Ennassik, Lahcen Maniar and Mohamed Aziz Taoudi

Abstract: In this paper we prove some new fixed point theorems in r-normed and locally r-convex spaces. Our conclusions generalize many well-known results and provide a partial affirmative answer to Schauder's conjecture. Based on the obtained results, we prove the analogue of a Von Neumann's theorem in locally r-convex spaces. In addition, an application to game theory is presented.

Key Words and Phrases: r-normed space, locally r-convex space, s-convex set, fixed point theorems, topological vector space, Schauder's conjecture.

2010 Mathematics Subject Classification: 47H10, 46A16, 46A50.

Published on-line: July 1st, 2021.

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