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中文摘要：
本文给出了一类广义压缩映射的一种连续方法，在完备度量空间中建立了一类非自映射的一个同伦定理．引入了一类广义扩张映射，给出了它们的不动点定理，并在一定的条件下证明了这些不动点构成了Banach空间中一个不可数的闭集．
英文摘要：
A continuation method for a class of generalized contractive mappings is given, which establishes a homotopy theorem for a class of non-self mappings in a complete metric space. In addition, a type of generalized expansive mappings is introduced and the corresponding fixed point theorem is proved. Finally, the analytical properties of the fixed points of such a generalized expansive mapping are investigated and it is proved that the set of such fixed points is uncountable and closed in a Banach space.
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