Let X be a strictly convex Banach space, whose predual space is \( Y (X=Y^{\prime })\), having the weak star sequentially compact unit ball for the topology \( \sigma (X, Y) \) and the weak star Kadec–Klee property. Furthermore, we suppose that the unit ball of the dual space \(X^{\prime }\) is weak star sequentially compact for the topology \(\sigma (X^{\prime }, X)\). Let C be a nonempty convex bounded closed subset of X; then every nonexpansive mapping \( T:C \rightarrow C \) has a fixed point. As consequences of this result, we generalize the Browder (Proc Natl Acad Sci USA 54:1041–1044, 1965) and Göhde (Math Nachr 301:251–258, 1965) theorems, where X is a uniformly convex Banach space and the Lin’s theorem by Lin (Nonlinear Anal 68:2303–2308, 2008) and Lin (J Math Anal Appl 362:534–541, 2010), where \( X=l^{1} \).

中文翻译：

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通过严格凸性和Kadec–Klee属性，Banach空间中的不动点属性

令X为严格凸的Banach空间，其先前空间为\（Y（X = Y ^ {\ prime}）\），具有拓扑为\（\ sigma（X，Y）\ ）和弱星Kadec–Klee属性。此外，我们假设对于拓扑\（\ sigma（X ^ {\ prime}，X）\），对偶空间\（X ^ {\ prime} \）的单位球是弱星，顺序压缩。令C为X的非空凸有界封闭子集；然后每个非扩展映射\（T：C \ rightarrow C \）有一个固定点。作为此结果的结果，我们推广了Browder定理（Proc Natl Acad Sci USA，54：1041–1044，1965）和Göhde定理（Math Nachr 301：251-258，1965）定理，其中X是一致凸的Banach空间，而Lin是Lin（非线性分析68：2303–2308，2008）和Lin（J Math Anal Appl 362：534–541，2010）定理，其中\（X = l ^ {1} \）。