In the present paper, we focus our attention on the existence of the fixed point for the sum of the cyclic contraction and the noncyclic accretive operator. Also, we study the best proximity point for the sum of two non-self-mappings. Moreover, we provide the existence of the best proximity point for the cyclic contraction through the notion of the nonlinear -set contraction. Finally, we give the existence of the best proximity point for the sum of the nonlinear -set contraction mapping and partially completely continuous mapping in the setting of the partially ordered complete normed linear space.

中文翻译：

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两个非自我操作者的总和的最佳邻近点

在本文中，我们将注意力集中在循环收缩和非循环增生算子之和的不动点的存在上。此外，我们研究两个非自映射之和的最佳接近点。此外，我们通过非线性的概念，提供最佳的临近点的循环收缩的存在-集压缩。最后，我们给出了最好的临近点为非线性的和存在-在部分有序完整赋范线性空间的设置集压缩映射和部分完全连续的映射。