Skip to main content
SpringerLink
Log in

Related Results on Stability of Functional Inequalities and Equations

  • Chapter
Stability of Functional Equations in Random Normed Spaces

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 86))

  • 691 Accesses

Abstract

In this chapter, we prove some stability results for certain functional inequalities and functional equations in latticetic random φ-normed spaces, r-divisible groups and homogeneous probabilistic (random) modular spaces.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
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. J. Aczél, Lectures on Functional Equations and Their Applications (Academic Press, New York, 1966)

    MATH  Google Scholar 

  2. J. Aczél, J. Dhombres, Functional Equations in Several Variables (Cambridge University Press, Cambridge, 1989)

    Book  MATH  Google Scholar 

  3. L. Cădariu, V. Radu, On the stability of the Cauchy functional equation: a fixed point approach. Grazer Math. Ber. 346, 43–52 (2004)

    MATH  Google Scholar 

  4. P.W. Cholewa, The stability problem for a generalized Cauchy type functional equation. Rev. Roum. Math. Pures Appl. 29, 457–460 (1984)

    MathSciNet  MATH  Google Scholar 

  5. J.K. Chung, P.K. Sahoo, On the general solution of a quartic functional equation. Bull. Korean Math. Soc. 40, 565–576 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Ebadian, A. Najati, M. Eshaghi Gordji, On approximate additive–quartic and quadratic–cubic functional equations in two variables on Abelian groups. Results Math. (2010). doi:10.1007/s00025-010-0018-4

    MathSciNet  Google Scholar 

  8. M. Eshaghi Gordji, Stability of a functional equation deriving from quartic and additive functions. Bull. Korean Math. Soc. 47, 491–502 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Eshaghi Gordji, M.B. Ghaemi, S.K. Gharetapeh, S. Shams, A. Ebadian, On the stability of J ∗-derivations. J. Geom. Phys. 60, 454–459 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. M. Eshaghi Gordji, S.K. Gharetapeh, C. Park, S. Zolfaghri, Stability of an additive–cubic–quartic functional equation. Adv. Differ. Equ. 2009, 395693 (2009), 20 pp.

    Google Scholar 

  11. M. Eshaghi Gordji, S.K. Gharetapeh, J.M. Rassias, S. Zolfaghari, Solution and stability of a mixed type additive, quadratic and cubic functional equation. Adv. Differ. Equ. 2009, 826130 (2009), 17 pp.

    Google Scholar 

  12. M. Eshaghi Gordji, H. Khodaei, On the generalized Hyers–Ulam–Rassias stability of quadratic functional equations. Abstr. Appl. Anal. 2009, 923476 (2009), 11 pp.

    MathSciNet  Google Scholar 

  13. W. Fechner, Stability of a functional inequalities associated with the Jordan–von Neumann functional equation. Aequ. Math. 71, 149–161 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. G.L. Forti, An existence and stability theorem for a class of functional equations. Stochastica 4, 22–30 (1980)

    Google Scholar 

  15. M.B. Ghaemi, M. Eshaghi Gordji, H. Majani, Approximately quintic and sextic mappings on the probabilistic normed spaces. Preprint

    Google Scholar 

  16. A. Gilányi, Eine zur Parallelogrammgleichung äquivalente Ungleichung. Aequ. Math. 62, 303–309 (2001)

    Article  MATH  Google Scholar 

  17. A. Gilányi, On a problem by K. Nikodem. Math. Inequal. Appl. 5, 707–710 (2002)

    MathSciNet  MATH  Google Scholar 

  18. O. Hadžić, E. Pap, V. Radu, Generalized contraction mapping principles in probabilistic metric spaces. Acta Math. Hung. 101, 131–148 (2003)

    Article  MATH  Google Scholar 

  19. K.W. Jun, H.M. Kim, The generalized Hyers–Ulam–Rassias stability of a cubic functional equation. J. Math. Anal. Appl. 274, 867–878 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  20. K.W. Jun, H.M. Kim, I.S. Chang, On the Hyers–Ulam stability of an Euler–Lagrange type cubic functional equation. J. Comput. Anal. Appl. 7, 21–33 (2005)

    MathSciNet  MATH  Google Scholar 

  21. S.M. Jung, Z.H. Lee, A fixed point approach to the stability of quadratic functional equation with involution. Fixed Point Theory Appl. 2008, 732086 (2008), 11 pp.

    MathSciNet  Google Scholar 

  22. S.M. Jung, S. Min, A fixed point approach to the stability of the functional equation f(x+y)=F[f(x),f(y)]. Fixed Point Theory Appl. 2009, 912046 (2009), 8 pp.

    Article  MathSciNet  Google Scholar 

  23. P. Kannappan, Quadratic functional equation and inner product spaces. Results Math. 27, 368–372 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  24. S. Lee, S. Im, I. Hwang, Quartic functional equations. J. Math. Anal. Appl. 307, 387–394 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  25. A. Najati, Hyers–Ulam–Rassias stability of a cubic functional equation. Bull. Korean Math. Soc. 44, 825–840 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  26. C. Park, Fixed points in functional inequalities. J. Inequal. Appl. 2008, 298050 (2008), pp. 8

    Article  Google Scholar 

  27. C. Park, Y. Cho, M. Han, Functional inequalities associated with Jordan–von Neumann type additive functional equations. J. Inequal. Appl. 2007, 41820 (2007)

    MathSciNet  Google Scholar 

  28. J. Rätz, On inequalities associated with the Jordan–von Neumann functional equation. Aequ. Math. 66, 191–200 (2003)

    Article  MATH  Google Scholar 

  29. F. Skof, Proprietà locali e approssimazione di operatori. Rend. Semin. Mat. Fis. Milano 53, 113–129 (1983)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Education, Department of Mathematics Education, Gyeongsang National University, Chinju, Republic of South Korea

    Yeol Je Cho

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

    Themistocles M. Rassias

  3. Department of Mathematics, Iran University of Science and Technology, Behshahr, Iran

    Reza Saadati

Authors
  1. Yeol Je Cho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Themistocles M. Rassias
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Reza Saadati
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Cho, Y.J., Rassias, T.M., Saadati, R. (2013). Related Results on Stability of Functional Inequalities and Equations. In: Stability of Functional Equations in Random Normed Spaces. Springer Optimization and Its Applications, vol 86. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8477-6_9

Download citation

Publish with us

Policies and ethics

Search

Navigation