Abstract

In a recent paper [I. Altun and A. Tasdemir, On best proximity points of interpolative proximal contractions, Quaestiones Math. (2020), DOI: 10.2989/16073606.2020.1785576] the authors proved two best proximity point theorems for a new class of non-self mappings, called interpolative Reich-Rus-Ćirić type proximal contractions of the first and second kinds. Our purpose is to show that their results follow from a fixed point theorem for interpolative Reich-Rus-Ćirić type contraction mappings [E. Karapinar, R. Agarwal and H. Aydi, Interpolative Reich-Rus-Ćirić contractions on partial metric spaces, Mathematics 6 (2018), 7 pages].

摘要

在最近的一篇论文中 [I. Altun 和 A. Tasdemir，关于插值近端收缩的最佳接近点，Quaestiones Math。(2020), DOI: 10.2989/16073606.2020.1785576] 作者为一类新的非自映射证明了两个最佳邻近点定理，称为第一类和第二类插值 Reich-Rus-Ćirić 型近端收缩。我们的目的是证明他们的结果遵循插值 Reich-Rus-Ćirić 类型收缩映射的不动点定理 [E. Karapinar、R. Agarwal 和 H. Aydi，部分度量空间上的插值 Reich-Rus-Ćirić 收缩，数学 6 (2018)，7 页]。