如果方程Tx=x不能解，則探索是否存在一個x與Tx盡可能的靠近的近似解，在度量空間的子集，定點理論是求方程式Tx=x有近似解必不可缺的工具。在本研究中，藉著使用米爾-基勒映射，坎南循環收縮和查特吉循環收縮，我們建立了有關單一函數T的米爾-基勒-坎南-查特吉循環收縮概念的新表示式,其中T是T:A∪B→A∪B，A,B是度量空間(X,d)的非空子集；我們也建立了有關兩個函數對T和S的米爾-基勒-坎南-查特吉循環收縮對概念的新表示式，其中T，S是T:A→B；S:B→A的(T,S)的映射。最後，我們證明了這兩種循環收縮型的表示式都存在最佳鄰近點定理，而我們的結果推廣或改進了許多最近文獻中有關最佳鄰近點定理的研究。

If the equation Tx=x does not find the solution.Fixed point theory is a essential instrument for solving the equation for a mapping defined on a subset of a metric space to explore the existence of an x that is as close to Tx as possible.In this study,by using the Meir-Keeler mapping, cyclic Kannan contraction and cyclic Chatterjee contraction, we establish the notions of cyclic Meir-Keeler-Kannan-Chatterjea contraction T:A∪B→A∪B and cyclic Meir-Keeler-Kannan-Chatterjea contractive pair (T;S) of mappings T:A→B and S:B→A, and then we prove some best proximity point theorems for these various types of cyclic contractions. Our results generalize or improve many recent best proximity point theorems in the literature.

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