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A NOTE ON BRØNDSTED’S FIXED POINT THEOREM

Part of: Nonlinear operators and their properties Normed linear spaces and Banach spaces; Banach lattices Topological linear spaces and related structures Ordered sets Equations and inequalities involving nonlinear operators

Published online by Cambridge University Press:  31 August 2023

OLEG ZUBELEVICH Open the ORCID record for OLEG ZUBELEVICH [Opens in a new window]
OLEG ZUBELEVICH*
Affiliation:
Steklov Mathematical Institute of the Russian Academy of Sciences, 2nd Krestovskii Pereulok 12-179, 129110, Moscow, Russia
*
e-mail: oezubel@gmail.com
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Abstract

We show that for the case of uniformly convex Banach spaces, the conditions of Brøndsted’s fixed point theorem can be relaxed.

Keywords

fixed pointspartial orderdiscontinuous operators

MSC classification

Primary: 47H10: Fixed-point theorems
Secondary: 06A06: Partial order, general 46A40: Ordered topological linear spaces, vector lattices 46B40: Ordered normed spaces 46B42: Banach lattices 47J05: Equations involving nonlinear operators (general)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 6
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The research was funded by a grant from the Russian Science Foundation (Project No. 19-71-30012).

References

Brøndsted, A., ‘On a lemma of Bishop and Phelps’, Pacific J. Math. 55 (1974), 335–341.CrossRefGoogle Scholar
Brøndsted, A., ‘Fixed points and partial orders’, Proc. Amer. Math. Soc. 60 (1976), 365–366.Google Scholar
Caristi, J. and Kirk, W. A., ‘Geometric fixed point theory and inwardness conditions’, in: The Geometry of Metric and Linear Spaces (Conference, Michigan State University, 1974), Lecture Notes in Mathematics, 490 (ed. Kelly, L. M.) (Springer, New York, 1975), 74–83.CrossRefGoogle Scholar
Yosida, K., Functional Analysis (Springer, New York, 1980).Google Scholar