Fixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spaces

Anthony To-Ming Lau, Yong Zhang

Abstract


It has been a long-standing problem posed by the first author in a conference in Marseille in 1990 to characterize semitopological semigroups which have common fixed point property when acting on a nonempty weak* compact convex subset of a dual Banach space as weak* continuous and norm nonexpansive mappings. Our investigation in the paper centers around this problem. Our main results rely on the well-known Ky Fan's inequality for convex functions.

Keywords


amenability; semigroups; non-expansive mappings; weak*-compact convex sets; common fixed point; invariant mean; submean

Mathematics Subject Classification (2010)


Primary: 43A07; Secondary 43A60, 22D05, 46B20.

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