Description

• Title:
  Fixed point theory on Banach spheres
• Creator:
  Kimura, Yasunori;
  Sudo, Shuta
• Description:
  In this paper, we consider and study the concept of the Banach sphere. The usual spherical distance of the unit sphere of a Hilbert space is defined by its inner product and the inverse of the cosine function. Therefore, we cannot apply this notion to Banach spheres in general. We first introduce a two-variable function like a spherical distance and a notion of convex combination on a Banach sphere. After that, we define a projection onto a subset of a Banach sphere, and prove a fixed point theorem and fixed point approximation for a mapping having a kind of nonspreadingness. Our work is a challenge to construct optimisation theory on spherical planes without geodesics.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2024 Yasunori Kimura, Shuta Sudo;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2024.09.25
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 64, No 2 (December 2024); 655 - 673;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/55393/39874 ;https://apcz.umk.pl/TMNA/article/view/55393/39875
• Subject:
  Banach sphere;
  fixed point theorem;
  shrinking projection method;
  47H10, 58C30
• Identifier: https://apcz.umk.pl/TMNA/article/view/55393
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other