Honam Mathematical Journal (호남수학학술지)

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A NOTE ON THE EXTENSION OF ε-ISOMETRIES ON THE UNIT SPHERE OF BANACH SPACES

  • Minanur Rohman (Department of Mathematics, Faculty of Science, Ondokuz Mayis Universitesi, Department of Madrasah Ibtidaiyah Teacher Education, School of Islamic Studies Ma'had Aly Al-Hikam Malang) ;
  • Ilker Eryilmaz (Department of Mathematics, Faculty of Science, Ondokuz Mayis Universitesi)
  • Received : 2023.05.04
  • Accepted : 2023.09.13
  • Published : 2024.03.20
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Abstract

Let X, Y be Banach spaces, SX and SY be the unit sphere of X and Y, respectively. Let f0 : SX → SY be ε-isometry for some ε ≥ 0. In this paper, we show that there is an extension f : X → Y of f0 such that f is linear.

Keywords

Acknowledgement

The authors thank OMU Functional Analysis and Function Theory Research Group (OFAFTReG) for meaningful discussions in this study. Special thank to Prof. Cenap Duyar, Prof. Birsen Duyar, and Dr. Halil Mutuk for their suggestions. The authors also thank the reviewers for their comments and suggestions in this article.

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