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On Exact and Approximate Orthogonalities Based on Norm Derivatives

  • Ali Zamani
  • Mahdi Dehghani
Chapter

Abstract

We survey mainly recent results on the orthogonality relations in normed linear spaces related to norm derivatives. We will focus on fundamental properties of norm derivatives orthogonality, differences and connections between these orthogonality types, and geometric results and problems closely related to them.

Keywords

Norm derivative Orthogonality Approximate orthogonality Orthogonality preserving mappings Approximate orthogonality preserving property Stability 

Mathematics Subject Classification (2010)

Primary 46B20; Secondary 46C50 47B49 

Notes

Acknowledgement

The authors would like to thank the referee for her/his valuable suggestions and comments.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ali Zamani
    • 1
  • Mahdi Dehghani
    • 2
  1. 1.Department of MathematicsFarhangian UniversityTehranIran
  2. 2.Department of Pure MathematicsFaculty of Mathematical Sciences, University of KashanKashanIran

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