Skip to main content
SpringerLink
Log in

Fixed Point and Nearly m-Dimensional Euler–Lagrange-Type Additive Mappings

  • Chapter
  • First Online:
Modern Discrete Mathematics and Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 131))

  • 1486 Accesses

Abstract

In this paper, using the fixed point alternative approach, we prove the generalized Hyers–Ulam–Rassias stability of the following Euler–Lagrange-type additive functional equation where \(r_1, \ldots , r_m \in \mathbb R\), \(\sum _{i=1}^{m}r_i\neq 0,\) and r i, r j ≠ 0 for some 1 ≤ i < j ≤ m in random normed spaces.

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 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
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  MathSciNet  Google Scholar 

  2. Cholewa, P.W.: Remarks on the stability of functional equations. Aequationes Math. 27, 76–86 (1984)

    Article  MathSciNet  Google Scholar 

  3. Czerwik, S.: Functional Equations and Inequalities in Several Variables. World Scientific, River Edge (2002)

    Google Scholar 

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

    Google Scholar 

  5. Gordji, M.E., Khodaei, H.: Stability of Functional Equations. Lap Lambert Academic Publishing, Tehran (2010)

    Google Scholar 

  6. Gordji, M.E., Savadkouhi, M.B.: Stability of mixed type cubic and quartic functional equations in random normed spaces. J. Inequal. Appl. 2009, 9 pp. (2009). Article ID 527462

    Google Scholar 

  7. Gordji, M.E., Zolfaghari, S., Rassias, J.M., Savadkouhi, M.B.: Solution and stability of a mixed type cubic and quartic functional equation in quasi-Banach spaces. Abstr. Appl. Anal. 2009, 14 pp. (2009). Article ID 417473

    Google Scholar 

  8. Gordji, M.E., Savadkouhi, M.B., Park, C.: Quadratic-quartic functional equations in RN-spaces. J. Inequal. Appl. 2009, 14 pp. (2009). Article ID 868423

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  11. Jung, S.-M., Rassias, M.Th.: A linear functional equation of third order associated to the Fibonacci numbers. Abstr. Appl. Anal. 2014, 7 pp. (2014). Article ID 137468

    Google Scholar 

  12. Jung, S.-M., Popa, D., Rassias, M.Th.: On the stability of the linear functional equation in a single variable on complete metric groups. J. Glob. Optim. 59, 165–171 (2014)

    Article  MathSciNet  Google Scholar 

  13. Jung, S.-M., Rassias, M.Th., Mortici, C.: On a functional equation of trigonometric type. Appl. Math. Comput. 252, 294–303 (2015)

    Article  MathSciNet  Google Scholar 

  14. Kenary, H.A., Cho, Y.J.: Stability of mixed additive-quadratic Jensen type functional equation in various spaces. Comput. Math. Appl. 61, 2704–2724 (2011)

    Google Scholar 

  15. Mihet, D., Radu, V.: On the stability of the additive Cauchy functional equation in random normed spaces. J. Math. Anal. Appl. 343, 567–572 (2008)

    Article  MathSciNet  Google Scholar 

  16. Park, C.: Generalized Hyers-Ulam-Rassias stability of n-sesquilinear-quadratic mappings on Banach modules over C ∗-algebras. J. Comput. Appl. Math. 180, 279–291 (2005)

    Google Scholar 

  17. Park, C., Hou, J., Oh, S.: Homomorphisms between JC -algebras and Lie C ∗-algebras. Acta Math. Sin. (Engl. Ser.) 21(6), 1391–1398 (2005)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  19. Rassias, Th.M.: On the stability of functional equations and a problem of Ulam. Acta Appl. Math. 62(1), 23–130 (2000)

    Google Scholar 

  20. Saadati, R., Park, C.: Non-Archimedean \(\mathcal {L}\)-fuzzy normed spaces and stability of functional equations. Comput. Math. Appl. 60, 2488–2496 (2010)

    Google Scholar 

  21. Saadati, R., Vaezpour, M., Cho, Y.J.: A note to paper “On the stability of cubic mappings and quartic mappings in random normed spaces”. J. Inequal. Appl. 2009 (2009). Article ID 214530. https://doi.org/10.1155/2009/214530

    Article  Google Scholar 

  22. Saadati, R., Zohdi, M.M., Vaezpour, S.M.: Nonlinear L-random stability of an ACQ functional equation. J. Inequal. Appl. 2011, 23 pp. (2011). Article ID 194394. https://doi.org/10.1155/2011/194394

    Article  MathSciNet  Google Scholar 

  23. Schewizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland Series in Probability and Applied Mathematics. North-Holland, New York (1983)

    Google Scholar 

  24. Skof, F.: Local properties and approximation of operators. Rend. Sem. Mat. Fis. Milano 53, 113–129 (1983)

    Google Scholar 

  25. Ulam, S.M.: Problems in Modern Mathematics, Science Editions. Wiley, New York (1964)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Yasouj University, Yasouj, Iran

    Hassan Azadi Kenary

Authors
  1. Hassan Azadi Kenary
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hassan Azadi Kenary .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Hellenic Military Academy, Vari, Greece

    Nicholas J. Daras

  2. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kenary, H.A. (2018). Fixed Point and Nearly m-Dimensional Euler–Lagrange-Type Additive Mappings. In: Daras, N., Rassias, T. (eds) Modern Discrete Mathematics and Analysis . Springer Optimization and Its Applications, vol 131. Springer, Cham. https://doi.org/10.1007/978-3-319-74325-7_11

Download citation

Publish with us

Policies and ethics

Search

Navigation