Kadec-Klee property in Musielak-Orlicz function spaces equipped with the Orlicz norm |
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Authors: | Cui Yunan Zhao Li |
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Affiliation: | 1.Department of Mathematics, Harbin University of Science and Technology, Harbin, 150080, China ; |
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Abstract: | 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. |
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