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The purpose of this paper is to present a new method for the research of best proximity point theorems of nonlinear mappings in metric spaces. In this paper, the P-operator technique, which changes non-self-mapping to self-mapping, provides a new and simple method of proof. Best proximity point theorems for weakly contractive and weakly Kannan mappings, generalized best proximity point theorems for generalized contractions, and best proximity points for proximal cyclic contraction mappings have been proved by using this new method. Meanwhile, many recent results in this area have been improved.

A new method for the research of best proximity point theorems of nonlinear mappings