# PROPERTIES $(U\~{A}_2)^*$ AND $(W\~{A}_2)$ IN ORLICZ SEQUENCE SPACES AND SOME OF THEIR CONSEQUENCES

Cui, Yunan and Hudzik, Henryk and Sims, Brailey PROPERTIES $(U\~{A}_2)^*$ AND $(W\~{A}_2)$ IN ORLICZ SEQUENCE SPACES AND SOME OF THEIR CONSEQUENCES. Journal of Mathematical Analysis and Applications . (Submitted)

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In this paper, we introduce a new geometric property $(U\~{A}_2)$ and we show that if a separable Banach space has this property, then both $X$ and its dual $X^*$ have the weak fixed point property. We also prove that a uniformly Gateaux differentiable Banach space has property $(U\~{A}_2)$ and that if $X^*$ has property $(U\~{A}_2)^*$, then $X$ has the $(UKK)$-property. Criteria for Orlicz spaces to have the properties $(UA^\epsilon_2), (UA^\epsilon_2)^*$ and $(NUS*$) are given.