Loading [MathJax]/jax/output/CommonHTML/jax.js
Journals
Resources
About Us
Open Access
Go to previous page

Approximation of the Cubic Functional Equations in Lipschitz Spaces

Approximation of the Cubic Functional Equations in Lipschitz Spaces

Year:    2014

Analysis in Theory and Applications, Vol. 30 (2014), Iss. 4 : pp. 354–362

Abstract

Let G be an Abelian group and let ρ:G×G[0,) be a metric on G. Let ε be a normed space. We prove that under some conditions if f:Gε is an odd function and Cx:Gε defined by Cx(y):=2f(x+y)+2f(xy)+12f(x) f(2x+y)f(2xy) is a cubic function for all xG, then there exists a cubic function C:Gε such that fC is Lipschitz. Moreover, we investigate the stability of cubic functional equation 2f(x+y)+2f(xy)+12f(x)f(2x+y) f(2xy)=0 on Lipschitz spaces.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2014.v30.n4.2

Analysis in Theory and Applications, Vol. 30 (2014), Iss. 4 : pp. 354–362

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    9

Keywords:    Cubic functional equation Lipschitz space stability.

  1. Almost tri-cubic functions with Lipschitz condition

    Nikoufar, Ismail

    Tbilisi Mathematical Journal, Vol. 13 (2020), Iss. 2

    https://doi.org/10.32513/tbilisi/1593223228 [Citations: 0]
  2. Stability of Generalized Multi-quadratic Mappings in Lipschitz Spaces

    Dashti, Mahshid | Khodaei, Hamid

    Results in Mathematics, Vol. 74 (2019), Iss. 4

    https://doi.org/10.1007/s00025-019-1083-y [Citations: 7]
  3. LIPSCHITZ CRITERIA FOR BI-QUADRATIC FUNCTIONAL EQUATIONS

    Nikoufar, Ismail

    Communications of the Korean Mathematical Society, Vol. 31 (2016), Iss. 4 P.819

    https://doi.org/10.4134/CKMS.c150249 [Citations: 5]
  4. Stability of Multi-Quadratic Functions in Lipschitz Spaces

    Nikoufar, Ismail

    Iranian Journal of Science and Technology, Transactions A: Science, Vol. 43 (2019), Iss. 2 P.621

    https://doi.org/10.1007/s40995-017-0478-4 [Citations: 5]
  5. Behavior of Bi-Cubic Functions in Lipschitz Spaces

    Nikoufar, Ismail

    Lobachevskii Journal of Mathematics, Vol. 39 (2018), Iss. 6 P.803

    https://doi.org/10.1134/S1995080218060136 [Citations: 2]
  6. Erratum to: Quartic functional equations in Lipschitz spaces

    Nikoufar, Ismail

    Rendiconti del Circolo Matematico di Palermo (1952 -), Vol. 65 (2016), Iss. 2 P.345

    https://doi.org/10.1007/s12215-015-0222-x [Citations: 4]