Skip to main content
SpringerLink
Log in

Stability of the equation of (p, q)-Wright functions

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

The Hyers–Ulam stability of a generalization of the functional equation of p-Wright affine functions in normed spaces is studied. We give sufficient conditions for stability of this equation with some class of control functions and discuss the optimality of obtained bounding constants in particular cases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Bahyrycz and M. Piszczek, Hyperstability of the Jensen functional equation, Acta Math. Hungar., 142 (2014), 353–365, DOI:10.1007/s10474-013-0347-3.

  2. J. Brzdȩk, J. Chudziak and Zs. Páles, A fixed point approach to stability of functional equations, Nonlinear Anal., 74 (2011), 6728–6732.

  3. J. Brzdȩk and K. Ciepliński, Hyperstability and superstability, Abstr. Appl. Anal., vol. 2013 (2013), Article ID 401756, 13 pages, DOI:10.1155/2013/401756.

  4. Brzdȩk J.: Stability of the equation of the p-Wright affine functions. Aequationes Math., 85, 497–503 (2013)

    Article  MathSciNet  Google Scholar 

  5. Chudziak J.: Approximate solutions of the Gołaȩb–Schinzel functional equation. J. Approx. Theory, 136, 21–25 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Z. Daróczy, K. Lajkó, R. L. Lovas, Gy. Maksa and Zs. Páles, Functional equations involving means, Acta Math. Hungar., 166 (2007), 79–87.

  7. A. Gilányi and Zs. Páles, On Dinghas-type derivatives and convex functions of higher order, Real Anal. Exchange, 27 (2001/2002), 485–493.

  8. D. H. Hyers, G. Isac and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser (Boston, 1998).

  9. S.-M. Jung, Hyers–Ulam–Rassias Stability of Functional Equations in Nonlinear Analysis, Springer Optimization and Its Applications, vol. 48, Springer (New York– Dordrecht–Heidelberg–London, 2011).

  10. Jung S.-M.: Hyers–Ulam–Rassias stability of Jensen’s equation and its application. Proc. Amer. Math. Soc., 126, 3137–3143 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  11. Gy. Maksa, K. Nikodem and Zs. Páles, Results on t-Wright convexity, C. R. Math. Rep. Acad. Sci. Canada, 13 (1991), 274–278.

  12. Moszner Z.: On the stability of functional equations. Aequationes Math., 77, 33–88 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. A. Najati and C. Park, Stability of homomorphisms and generalized derivations on Banach algebras, J. Inequal. Appl., vol. 2009 (2009), Article ID 595439, 12 pages, DOI:10.1155/2009/595439.

  14. B. Paneah, A new approach to the stability of linear functional operators, Aequationes Math., 78 (2009), 45–61.

  15. M. Piszczek, Remark on hyperstability of the general linear equation, Aequationes Math., 88 (2014), 163–168, DOI:10.1007/s00010-013-0214-x.

  16. Sikorska J.: On a direct method for proving the Hyers–Ulam stability of functional equations. J. Math. Anal. Appl., 372, 99–109 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  17. Wright E.M.: An inequality for convex functions. Amer. Math. Monthly, 61, 620–622 (1954)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Pedagogical University, Podchoraȩżych 2, 30–084, Kraków, Poland

    A. Bahyrycz & J. Olko

Authors
  1. A. Bahyrycz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Olko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Olko.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bahyrycz, A., Olko, J. Stability of the equation of (p, q)-Wright functions. Acta Math. Hungar. 146, 71–85 (2015). https://doi.org/10.1007/s10474-015-0477-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-015-0477-x

Key words and phrases

Mathematics Subject Classification

Search

Navigation