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摘要

本文研究了乘法度量空间上不动点唯一性的几个定理。首先,利用涉及到的乘法连续函数,分析了完全乘法度量空间上不动点唯一性定理的证明。然后,在不涉及乘法连续函数的情况下,分析了几个不动点唯一性定理。在包含乘积连续函数的完全乘法度量空间上,不动点唯一性定理的证明可以不需要缩乘映射。如果该映射满足包含乘法连续函数的条件,则证明了它具有唯一不动点。此外,在不涉及乘法连续函数的完全乘法度量空间上,不动点唯一性定理的证明可以通过要求映射是收缩来完成。
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ANALISIS BEBERAPA TEOREMA KETUNGGALAN TITIK TETAP DI RUANG METRIK MULTIPLIKATIF (MULTIPLICATIVE METRIC SPACES)
This research was conducted to analyze several theorems about fixed point uniqueness on multiplicative metric space. Firstly, the proof of fixed point uniqueness theorem on complete multiplicative metric space is analyzed with involving multiplicative continuous functions. Then, several fixed point uniqueness theorems is analyzed without involving multiplicative continuous functions. The proof of fixed point uniqueness theorem on complete multiplicative metric space with involving multiplicative continuous functions can be done without requirement of contraction multiplicative mapping. If this mapping is satisfying a condition with involving multiplicative continuous functions then it was proven that it had the unique fixed point. Furthermore, the proof of fixed point uniqueness theorem on complete multiplicative metric space without involving multiplicative continuous functions can be done by requiring the mapping is contraction.
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