Skip to main content
SpringerLink
Log in

Fuzzy Stability of a Quadratic-Additive Type Functional Equation

  • Chapter
Nonlinear Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 68))

  • 2171 Accesses

Abstract

In this paper, we investigate a fuzzy version of stability for the functional equation

$$2f(x+y)+f(x-y)+f(y-x)-f(2x)-f(2y) =0 $$

in the sense of M. Mirmostafaee and M.S. Moslehian.

Dedicated to Professor Themistocles M. Rassias on the occasion of his 60th birthday.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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. Jpn. 2, 64–66 (1950)

    Article  MATH  Google Scholar 

  2. Bag, T., Samanta, S.K.: Finite dimensional fuzzy normed linear spaces. J. Fuzzy Math. 11(3), 687–705 (2003)

    MathSciNet  MATH  Google Scholar 

  3. Cheng, S.C., Mordeson, J.N.: Fuzzy linear operator and fuzzy normed linear spaces. Bull. Calcutta Math. Soc. 86, 429–436 (1994)

    MathSciNet  MATH  Google Scholar 

  4. Czerwik, S.: On the stability of the quadratic mapping in normed spaces. Abh. Math. Semin. Univ. Hamb. 62, 59–64 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  5. 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 

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

    Article  MathSciNet  Google Scholar 

  7. Jun, K.-W., Lee, Y.-H.: A generalization of the Hyers–Ulam–Rassias stability of the pexiderized quadratic equations, II. Kyungpook Math. J. 47, 91–103 (2007)

    MathSciNet  MATH  Google Scholar 

  8. Katsaras, A.K.: Fuzzy topological vector spaces II. Fuzzy Sets Syst. 12, 143–154 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kim, G.-H.: On the stability of functional equations with square-symmetric operation. Math. Inequal. Appl. 4, 257–266 (2001)

    MathSciNet  MATH  Google Scholar 

  10. Kim, H.-M.: On the stability problem for a mixed type of quartic and quadratic functional equation. J. Math. Anal. Appl. 324, 358–372 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kramosil, I., Michalek, J.: Fuzzy metric and statistical metric spaces. Kybernetica 11, 326–334 (1975)

    MathSciNet  Google Scholar 

  12. Lee, Y.-H.: On the Hyers–Ulam–Rassias stability of the generalized polynomial function of degree 2. J. Chuncheong Math. Soc. 22, 201–209 (2009)

    Google Scholar 

  13. Lee, Y.-H.: On the stability of the monomial functional equation. Bull. Korean Math. Soc. 45, 397–403 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lee, Y.H., Jun, K.W.: A generalization of the Hyers–Ulam–Rassias stability of Jensen’s equation. J. Math. Anal. Appl. 238, 305–315 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  15. Lee, Y.H., Jun, K.W.: A generalization of the Hyers–Ulam–Rassias stability of Pexider equation. J. Math. Anal. Appl. 246, 627–638 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lee, Y.H., Jun, K.W.: On the stability of approximately additive mappings. Proc. Am. Math. Soc. 128, 1361–1369 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  17. Mirmostafaee, A.K., Moslehian, M.S.: Fuzzy almost quadratic functions. Results Math. 52, 161–177 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mirmostafaee, A.K., Moslehian, M.S.: Fuzzy versions of Hyers–Ulam–Rassias theorem. Fuzzy Sets Syst. 159, 720–729 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  20. Skof, F.: Local properties and approximations of operators. Rend. Semin. Mat. Fis. Milano 3, 113–129 (1983)

    Article  MathSciNet  Google Scholar 

  21. Ulam, S.M.: A Collection of Mathematical Problems, p. 63. Interscience, New York (1968)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics Education, Gongju National University of Education, Gongju, 314-711, Republic of Korea

    Sun-Sook Jin & Yang-Hi Lee

Authors
  1. Sun-Sook Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yang-Hi Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yang-Hi Lee .

Editor information

Editors and Affiliations

  1. , Department of Industrial & Systems Engin, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

  2. Center for Applied Optimization, Dept. Industrial & Systems, University of Florida, Weil Hall 303, Gainesville, 32611-6595, Florida, USA

    Pando G. Georgiev

  3. , Department of Mathematics & Statistics, University of Victoria, Finnerty Road 3800, Victoria, V8W 3R4, British Columbia, Canada

    Hari M. Srivastava

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Jin, SS., Lee, YH. (2012). Fuzzy Stability of a Quadratic-Additive Type Functional Equation. In: Pardalos, P., Georgiev, P., Srivastava, H. (eds) Nonlinear Analysis. Springer Optimization and Its Applications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3498-6_19

Download citation

Publish with us

Policies and ethics

Search

Navigation