Skip to main content
SpringerLink
Log in

Stability of the Pexiderized Cauchy Functional Equation in Non-Archimedean Spaces

  • Chapter
  • First Online:
Functional Equations in Mathematical Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 52))

  • 1577 Accesses

Abstract

In this paper, we investigate the Hyers–Ulam–Rassias stability of the Pexiderized Cauchy functional equation in non-Archimedean spaces.

Mathematics Subject Classification (2000): Primary 39B22, 39B82, 46S10

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aoki, T.: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan 2, 64–66 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brzdȩk, J.: On a method of proving the Hyers–Ulam stability of functional equations on restricted domains. Aust. J. Math. Anal. Appl. 6, no. 1, Art. 4, 10 pp. (2009)

    Google Scholar 

  3. Brzdȩk, J.: On the quotient stability of a family of functional equations. Nonlinear Anal. 71, 4396–4404 (2009)

    Article  MathSciNet  Google Scholar 

  4. Czerwik, S.: Functional Equations and Inequalities in Several Variables. World Scientific, New Jersey–London–Singapore–Hong Kong (2002)

    Google Scholar 

  5. Eskandani, G.Z.: On the Hyers-Ulam-Rassias stability of an additive functional equation in quasi-Banach spaces. J. Math. Anal. Appl. 345, 405–409 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gajda, Z.: On stability of additive mappings. Int. J. Math. Math. Sci. 14, 431–434 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  7. Găvruta, P.: A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184, 431–436 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  8. Găvruta, P.: An answer to question of John M. Rassias concerning the stability of Cauchy equation. In: Rassias, J.M. (ed.) Advances in Equations and Inequalities, pp. 67–71. Hadronic Press, Palm Harbor (1999)

    Google Scholar 

  9. Găvruta, P.: On a problem of G. Isac and Th. M. Rassias concerning the stability of mappings. J. Math. Anal. Appl. 261, 543–553 (2001)

    Article  MATH  Google Scholar 

  10. Găvruta, P.: On the Hyers-Ulam-Rassias stability of mappings. In: Milovanovic, G.V. (ed.) Recent Progress in Inequalities, pp. 465–469. Kluwer (1998)

    Google Scholar 

  11. Găvruta, P., Hossu, M., Popescu D., Căprău, C.: On the stability of mappings and an anwser to a problem of Th.M Rassias. Ann. Math. Blaise Pascal 2, 55–60 (1995)

    Google Scholar 

  12. Hensel, K.: Über eine neue Begründung der Theorie der algebraischen Zahlen. Jahresber. Deutsch. Math. Verein 6, 83–88 (1897)

    Google Scholar 

  13. Hyers, D.H.: On the stability of the linear functional equation. Proc. Nat. Acad. Sci. 27, 222–224 (1941)

    Article  MathSciNet  Google Scholar 

  14. Hyers, D.H., Isac G., Rassias, Th.M.: Stability of Functional Equations in Several Variables. Birkhäuser, Basel (1998)

    Book  MATH  Google Scholar 

  15. Isac, G., Rassias, Th.M.: Stability of ψ-additive mappings: Applications to nonlinear analysis. Int. J. Math. Math. Sci. 19, 219–228 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  16. Isac, G., Rassias, Th.M.: Functional inequalities for approximately additive mappings. In: Rassias, Th.M., Tabor, J. (eds.) Stability of Mappings of Hyers–Ulam Type, pp. 117–125. Hadronic Press, Palm Harbour (1994)

    Google Scholar 

  17. Jun, K., Lee, Y.: On the Hyers–Ulam–Rassias stability of a Pexiderized quadratic inequality. Math. Inequal. Appl. 4, 93–118 (2001)

    MathSciNet  MATH  Google Scholar 

  18. Jung, S.-M.: Hyers–Ulam–Rassias Stability of Functional Equations in Mathimatical Analysis. Hadronic Press, Palm Harbor (2001)

    Google Scholar 

  19. Kannappan, PL.: Quadratic functional equation and inner product spaces. Results Math. 27, 368–372 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  20. Moradlou, F., Vaezi, H., Eskandani, G.Z.: Hyers–Ulam–Rassias stability of a quadratic and additive functional equation in quasi-Banach spaces. Mediterr. J. Math. 6, 233–248 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Moslehian, M.S., Rassias, Th.M.: Stability of functional equation in non-Archimedean spaces. Appl. Anal. Discrete Math. 1, 325–334 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  22. Park, C., Moradlou, F.: Stability of Homomorphisms and Derivations in C*-ternary Rings. Taiwanese J. Math. 13, 1985–1999 (2009)

    MathSciNet  MATH  Google Scholar 

  23. Rassias, J.M.: On approximation of approximately linear mappings by linear mappings. J. Funct. Anal. 46 126–130 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  24. Rassias, J.M.: On approximation of approximately linear mappings by linear mappings. Bull. Sci. Math. 108, 445–446 (1984)

    MathSciNet  MATH  Google Scholar 

  25. Rassias, J.M.: Solution of a problem of Ulam. J. Approx. Theory 57, 268–273 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  26. Rassias, Th.M.: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72, 297–300 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  27. Rassias, Th.M.: On a modified Hyers–Ulam sequence. J. Math. Anal. Appl. 158, 106–113 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  28. Rassias, Th.M.: Problem 16. In: Report of the 27th International Symposium on Functional Equations, p. 309. Aequationes Math. 39, 292–293 (1990)

    Google Scholar 

  29. Rassias, Th.M.: On the stability of the quadratic functional equation and its applications. Studia Univ. Babeş-Bolyai Math. 43, 89–124 (1998)

    MATH  Google Scholar 

  30. Rassias, Th.M. (ed.): Functional Equations and Inequalities. Kluwer Academic Publishers, Dordrecht–Boston–London (2000)

    Google Scholar 

  31. Rassias, Th.M., S̆emrl, P.: On the behaviour of mappings which do not satisfy Hyers-Ulam stability. Proc. Amer. Math. Soc. 114 989–993 (1992)

    Google Scholar 

  32. Robert, A.M.: A Course in p-adic Analysis. Springer-Verlag, New York (2000)

    Book  MATH  Google Scholar 

  33. Ulam, S.M.: A Collection of the Mathematical Problems. Interscience Publ., New York (1960)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

    G. Zamani Eskandani

  2. Department of Mathematics, University Politechnica of Timisoara, Piata Victoriei, No. 2, 300006, Timisoara, Romania

    Paşc Găvruţa

Authors
  1. G. Zamani Eskandani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paşc Găvruţa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Zamani Eskandani .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, National Technical University of Athens, Iroon Polytechneiou 9, Athens, 15780, Greece

    Themistocles M. Rassias

  2. Institute of Mathematics, Pedagogical University, ul. Podchorazych 2, Krakow, 30-084, Poland

    Janusz Brzdek

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Eskandani, G.Z., Găvruţa, P. (2011). Stability of the Pexiderized Cauchy Functional Equation in Non-Archimedean Spaces. In: Rassias, T., Brzdek, J. (eds) Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications(), vol 52. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0055-4_24

Download citation

Publish with us

Policies and ethics

Search

Navigation