Existence of unique fixed point of a mapping defined on an uniquely remotal subset in Hilbert space

Som S., SAVAŞ E.

Journal of Analysis, vol.30, no.2, pp.547-556, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.1007/s41478-021-00361-2
  • Journal Name: Journal of Analysis
  • Journal Indexes: Scopus
  • Page Numbers: pp.547-556
  • Keywords: Continuity, Farthest point map, Maximizing sequence, Unbounded modulus function, Uniquely remotal
  • Uşak University Affiliated: Yes

Abstract

In this paper we introduce the notion of f-partial statistical continuity of a function (where f is an unbounded modulus function) which is much weaker than continuity of a function. We give an example to show that f-partial statistical continuity is weaker than continuity. Then we apply unbounded modulus function to give some answers to farthest point problem in real normed linear space which improves the result in [12]. As an application, we provide a sufficient condition for the existence of an unique fixed point of a self mapping defined on a non-empty, closed, bounded uniquely remotal subset in Hilbert space. Lastly, we introduce the notion of f-statistically maximizing sequence of a non-empty bounded subset M of a normed linear space X and show by an example that this notion is weaker than maximizing sequence.