Uniformly Lipschitzian Semigroups in Hilbert Space

1 June 1982

journal article
Published by Canadian Mathematical Society in Canadian Mathematical Bulletin

Vol. 25 (2) , 210-214
https://doi.org/10.4153/cmb-1982-029-5

Abstract

Let K be a closed, bounded, convex, nonempty subset of a Hilbert Space . It is shown that if is a left reversible, uniformly k-lipschitzian semigroup of mappings of K into itself, with k < √2, then has a common fixed point in K.

Keywords

UNIFORMLY LIPSCHITZIAN
LIPSCHITZIAN SEMIGROUPS
HILBERT SPACE
FIXED POINT
COMMON FIXED
NONEMPTY SUBSET
CONVEX

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Uniformly Lipschitzian Families of Transformations in Banach Spaces
Canadian Journal of Mathematics, 1974
A fixed point theorem for transformations whose iterates have uniform Lipschitz constant
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A Course on Optimization and Best Approximation
Lecture Notes in Mathematics, 1972
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