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In this paper, we consider a self map q defined on the union of two subsets E and F of a topological vector space. We proved the existence and uniqueness of fixed point for cyclic topologically r-contraction map q on \(E\cup F\) . Also we proved the existence and uniqueness of best proximity point for cyclic topologically contraction map q on \(E\cup F\) . In addition, we show that for any \(u_0\) in E and \(u_{i+1}=qu_i\) , the sequence \(\{u_{2i}\}\) converges to the best proximity point.

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Best Proximity Point Theorems in Topological Vector Spaces

  • 会议论文

  • 发表日期：

    2025年

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  • S. Sahayarajjoseph Nirmalkumar,
  • S. Sujith

摘要

In this paper, we consider a self map q defined on the union of two subsets E and F of a topological vector space. We proved the existence and uniqueness of fixed point for cyclic topologically r-contraction map q on \(E\cup F\) . Also we proved the existence and uniqueness of best proximity point for cyclic topologically contraction map q on \(E\cup F\) . In addition, we show that for any \(u_0\) in E and \(u_{i+1}=qu_i\) , the sequence \(\{u_{2i}\}\) converges to the best proximity point.