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Strong and pure fixed point properties of mappings on normed spaces

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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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Authors and Affiliations

  1. Department of Engineering Science, Bandırma Onyedi Eylül University, 10200, Bandırma, Balıkesir, Turkey

    Hüseyin Işık

  2. Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran

    Vahid Parvaneh

  3. Faculty of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran

    Mohammad Reza Haddadi

Authors
  1. Hüseyin Işık
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  2. Vahid Parvaneh
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  3. Mohammad Reza Haddadi
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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 15, 305–309 (2021). https://doi.org/10.1007/s40096-021-00380-x

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  • DOI: https://doi.org/10.1007/s40096-021-00380-x

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