Strong and pure fixed point properties of mappings on normed spaces

Abstract

In this paper, the concept of strong fixed point property of a mapping is defined. The relationship between an approximating fixed point sequence and compactness is studied. The notion of a center set for a mapping is introduced. Some necessary and sufficient conditions for existence of mappings admitting a center set are presented. The results proved herein extend, generalize and improve some well-known comparable results.

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Correspondence to Hüseyin Işık or Mohammad Reza Haddadi.

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Işık, H., Parvaneh, V. & Haddadi, M.R. Strong and pure fixed point properties of mappings on normed spaces. Math Sci (2021). https://doi.org/10.1007/s40096-021-00380-x

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Keywords

  • Approximating fixed point sequence
  • Best approximation
  • Fixed point

Mathematics Subject Classification

  • 46A32
  • 46M05
  • 41A17