Sadovskii's fixed point theorem without convexity

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Abstract

The abstract formulation of Kirk's fixed point theorem by Penot played a major role in developing fixed point theorems in nonconvex setting. In this work, we similarly give an abstract formulation to Sadovskii's fixed point theorem using convexity structures. As an example, we discuss these new ideas in the hyperconvex metric setting.

Original languageBritish English
Pages (from-to)829-837
Number of pages9
JournalNonlinear Analysis, Theory, Methods and Applications
Volume53
Issue number6
DOIs
StatePublished - Jun 2003

Keywords

  • Condensing mappings
  • Fixed point
  • Hyperconvex
  • Measure of noncompactness
  • Nonexpansive mappings

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