It is well-known that the Kadec-Klee property is an important property in the geometry of Banach spaces. It is closely connected with the approximation compactness and fixed point property of non-expansive mappings. In this paper, a criterion for Musielak-Orlicz function spaces equipped with the Orlicz norm to have the Kadec-Klee property are given. As a corollary, we obtain that a class of non-reflexive Musielak-Orlicz function spaces have the Fixed Point property.

中文翻译：

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配备 Orlicz 范数的 Musielak-Orlicz 函数空间中的 Kadec-Klee 性质

众所周知，Kadec-Klee 性质是 Banach 空间几何中的一个重要性质。它与非扩张映射的近似紧致性和不动点性质密切相关。在本文中，给出了配备 Orlicz 范数的 Musielak-Orlicz 函数空间具有 Kadec-Klee 性质的判据。作为推论，我们得到一类非自反的 Musielak-Orlicz 函数空间具有不动点性质。