Best proximity pair results are proved for noncyclic relatively u-continuous condensing mappings. In addition, best proximity points of upper semicontinuous mappings are obtained which are also fixed points of noncyclic relatively u-continuous condensing mappings. It is shown that relative u-continuity of is a necessary condition that cannot be omitted. Some examples are given to support our results.

中文翻译：

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压缩映射和最佳邻近点结果

对于非循环的相对u连续的压缩映射，证明了最佳接近对结果。另外，获得了上半连续映射的最佳邻近点，它们也是非循环相对u-连续压缩映射的固定点。结果表明，的相对u连续性是一个不可忽略的必要条件。给出了一些例子来支持我们的结果。