A note on remotal and uniquely remotal sets in normed linear spaces

Uddalak Mukherjee; Sumit Som

A note on remotal and uniquely remotal sets in normed linear spaces

Functional Analysis 2025-10-14 v1

Authors: Uddalak Mukherjee , Sumit Som

Abstract

Remotal and uniquely remotal sets play an important role in the area of farthest point problem as well as nearest point problem in a Banach space $X.$ In this study, we find some sufficient conditions for remotality and uniquely remotality of a bounded subset of a Banach space $X$ through $\alpha\beta$ -statistical convergence.

Keywords

remotal sets uniquely remotal sets Banach space normed linear space αβ-statistical convergence farthest point problem

Cite

@article{arxiv.2510.10992,
  title  = {A note on remotal and uniquely remotal sets in normed linear spaces},
  author = {Uddalak Mukherjee and Sumit Som},
  journal= {arXiv preprint arXiv:2510.10992},
  year   = {2025}
}

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