Bulletin of the Belgian Mathematical Society - Simon Stevin

Fixed point properties for semigroups of non-expansive mappings in conjugate Banach spaces

Khadime Salame

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In this paper we study common fixed point properties of non-linear actions of semi-topological semigroups on non-void weak* compact convex sets in dual Banach spaces. Among other things, we derive from our main result Theorem 1, the existence of a common fixed point property for semigroups of non-expansive mappings acting on non-empty weakly compact convex sets, generalizing a result of Hsu [13], Mitchell [25].

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 23, Number 4 (2016), 529-544.

First available in Project Euclid: 6 December 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]

amenable semigroups asymptotic normal structure fixed point properties left reversible semigroups non-expansive mappings normal structure


Salame, Khadime. Fixed point properties for semigroups of non-expansive mappings in conjugate Banach spaces. Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 4, 529--544. doi:10.36045/bbms/1480993585. https://projecteuclid.org/euclid.bbms/1480993585

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