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ON MODULATED TOPOLOGICAL VECTOR SPACES AND APPLICATIONS

Part of: Normed linear spaces and Banach spaces; Banach lattices Nonlinear operators and their properties

Published online by Cambridge University Press:  10 July 2019

WOJCIECH M. KOZLOWSKI Open the ORCID record for WOJCIECH M. KOZLOWSKI [Opens in a new window]
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
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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.

Keywords

topological vector spacesBanach spacesmodular spacesmodular function spacesfixed pointsnonexpansive mappingsnormal structure

MSC classification

Primary: 47H09: Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.
Secondary: 46B20: Geometry and structure of normed linear spaces 47H10: Fixed-point theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 2 , April 2020 , pp. 325 - 332
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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