Note on Nonlinear Contraction Semigroups

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Apr 1969Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 21, page 219 (issn: 0002-9939,

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Authors: Miyadera, Isao;

doi: 10.2307/2036898 , 10.1090/s0002-9939-1969-0238123-5

Note on Nonlinear Contraction Semigroups

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Abstract

1. Let X be a Banach space and let { F(£); 0^£< » } be a family of nonlinear operators from X into itself satisfying the following conditions: (i) T(0)=I (the identity) and T{£+7]) = T{£)T{v) for ?, t?^0. (ii) ||r(£)x-7X£);y||=g||x-3,|| for x, y EX. (iii) limj_o+ ||F(£)x — x|| =0 for xEX. It is clear that for any fixed xEX, T{ii)x is strongly continuous in ?2;0. Such a family JF(£); 0:S£< °o ] is called a nonlinear contraction semigroup. Then we define the infinitesimal generator A of {F(£);0^<~} by

Keywords

functional analysis

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