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ON MODULATED TOPOLOGICAL VECTOR SPACES AND APPLICATIONS

Published online by Cambridge University Press:  10 July 2019

WOJCIECH M. KOZLOWSKI*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia email w.m.kozlowski@unsw.edu.au

Abstract

We introduce a notion of modulated topological vector spaces, that generalises, among others, Banach and modular function spaces. As applications, we prove some results which extend Kirk’s and Browder’s fixed point theorems. The theory of modulated topological vector spaces provides a very minimalist framework, where powerful fixed point theorems are valid under a bare minimum of assumptions.

Type
Research Article
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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