关于周界收缩的最佳近似点结果

多边形上的周长压缩及相关不动点定理

Perimetric Contraction on Polygons and Related Fixed Point Theorems

本文定义 $k$ 边形上的周长压缩与 Kannan 型周长压缩映射，在完备度量空间中证明其不动点存在及唯一性条件，并推广 Banach 定理。

A note on best proximity point for proximal contraction

In the year 2011, S.Basha \cite{BS} introduced the notion of proximal contraction in a metric space $X$ and study the existence and uniqueness of best proximity point for this class of mappings. Also, the author gave an algorithm to achieve this best proximity point. In this paper, we show that the best proximity point theorem can be proved by Banach contraction principle.

A remark on the paper "A note on the paper Best proximity point results for $p$-proximal contractions"

Recently, In the year 2020, Altun et al. \cite{AL} introduced the notion of $p$-proximal contractions and discussed about best proximity point results for this class of mappings. Then in the year 2021, Gabeleh and Markin \cite{GB} showed that the best proximity point theorem proved by Altun et al. in \cite{AL} follows from the fixed point theory. In this short note, we show that if the $p$-proximal contraction constant $k<\frac{1}{3}$ then the existence of best proximity point for $p$-proximal contractions follows from the celebrated Banach contraction principle.

A note on the paper "Best proximity point of generalized $F$-proximal non-self contractions

In the year 2021, Beg et al. \cite{beg} [J. Fixed Point Theory Appl.(2021)] introduced two classes of non-self mappings namely, generalized $F$-proximal contraction of the first kind and generalized $F$-proximal contraction of the second kind. Then authors studied the existence and uniqueness of best proximity points for this two classes of mappings. In this short note, we show that the existence of best proximity point for generalized $F$-proximal contraction of the first kind follows from the same conclusion in fixed point theory.

Best proximity point results in topological spaces and extension of Banach contraction principle

In this paper, we introduce the notion of topologically Banach contraction mapping defined on an arbitrary topological space X with the help of a continuous function $g:X\times X\rightarrow \mathbb{R}$ and investigate the existence of fixed points of such mapping. Moreover, we introduce two types of mappings defined on a non-empty subset of X and produce sufficient conditions which will ensure the existence of best proximity points for these mappings. Our best proximity point results also extend some existing results from metric spaces or Banach spaces to topological spaces. More precisely, ou…

Tripartite coincidence-best proximity points in generalized metric spaces

We first introduce a notion of convex structure in generalized metric spaces, then we introduce tripartite contractions, tripartite semi-contractions, tripartite coincidence points, as well as tripartite best proximity points for a given triple $(K;S;T)$ of nonlinear mappings defined on the union $A\cup B\cup C$ of closed subsets of a generalized metric space. We prove theorems on the existence and convergence of tripartite coincidence-best proximity points.