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Approximate Roberts orthogonality sets and \({(\delta, \varepsilon)}\)-(a, b)-isosceles-orthogonality preserving mappings

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Abstract

We introduce the concept of approximate Roberts orthogonality set and investigate the geometric properties of such sets. In addition, we introduce the notion of approximate a-isosceles-orthogonality and consider a class of mappings, which approximately preserve a-isosceles-orthogonality.

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References

  1. Alonso J., Martini H., Wu S.: On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces. Aequationes Math. 83, 153–189 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alsina C., Sikorska J., Tomás M.S.: Norm Derivatives and Characterizations of Inner Product Spaces. World Scientific, Hackensack (2009)

    Book  MATH  Google Scholar 

  3. Chmieliński, J.: On an \({\varepsilon}\)-Birkhoff orthogonality. J. Inequal. Pure Appl. Math. 6(3), Art. 79 (2005)

  4. Chmieliński J.: Linear mappings approximately preserving orthogonality. J. Math. Anal. Appl. 304, 158–169 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chmieliński J., Wójcik P.: Isosceles-orthogonality preserving property and its stability. Nonlinear Anal. 72, 1445–1453 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chmieliński J.: Normed spaces equivalent to inner product spaces and stability of functional equations. Aequationes Math. 87, 147–157 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chorianopoulos Ch., Psarrakos P.: Birkhoff–James approximate orthogonality sets and numerical ranges. Linear Algebra Appl. 434, 2089–2108 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dadipour, F., Sadeghi, F., Salemi, A.: An orthogonality in normed linear spaces based on angular distance inequality. Aequationes Math. doi:10.1007/s00010-014-0333-z

  9. Kong L., Cao H.: Stability of orthogonality preserving mapping and the orthogonality equation. J. Shaanxi Normal Univ. Nat. Sci. Ed. 36(5), 10–14 (2008)

    MathSciNet  MATH  Google Scholar 

  10. Sikorska J.: Orthogonalities and functional equations. Aequationes Math. 89, 215–277 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  11. Turnšek A.: On mappings approximately preserving orthogonality. J. Math. Anal. Appl. 336(1), 625–631 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wójcik P.: Linear mappings approximately preserving orthogonality in real normed spaces. Banach J. Math. Anal. 9(2), 134–141 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zamani A., Moslehian M.S.: Approximate Roberts orthogonality. Aequationes Math. 89, 529–541 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang Y., Chen Y., Hadwin D., Kong L.: AOP mappings and the distance to the scalar multiples of isometries. J. Math. Anal. Appl. 431(2), 1275–1284 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Pure Mathematics, Center of Excellence in Analysis on, Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, 91775, Iran

    Ali Zamani & Mohammad Sal Moslehian

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  1. Ali Zamani
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  2. Mohammad Sal Moslehian
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Correspondence to Mohammad Sal Moslehian.

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Zamani, A., Moslehian, M.S. Approximate Roberts orthogonality sets and \({(\delta, \varepsilon)}\)-(a, b)-isosceles-orthogonality preserving mappings. Aequat. Math. 90, 647–659 (2016). https://doi.org/10.1007/s00010-015-0383-x

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  • DOI: https://doi.org/10.1007/s00010-015-0383-x

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