<abstract xmlns="http://www.w3.org/1999/xhtml">We establish some stability results concerning the general cubic functional equationf(x + ky) - kf(x + y) + kf(x - y) - f(x - ky) = 2k(k2 - 1)f(y)for fixed k ℕ\{1} in the fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately cubic function can be approximated by a cubic mapping in a fuzzy sense and we establish that the existence of a solution for any approximately cubic mapping guarantees the completeness of the fuzzy normed spaces</abstract>

We establish some stability results concerning the general cubic functional equationf(x + ky) - kf(x + y) + kf(x - y) - f(x - ky) = 2k(k2 - 1)f(y)for fixed k ℕ\{1} in the fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately cubic function can be approximated by a cubic mapping in a fuzzy sense and we establish that the existence of a solution for any approximately cubic mapping guarantees the completeness of the fuzzy normed spaces

Stability of General Cubic Mapping in Fuzzy Normed Spaces

Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran

Pedagogical Department National and Capodistrian University of Athens 4, Agamemnonos Str., Aghia Paraskevi, Attikis 15342, Athens, Greece

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Stability of General Cubic Mapping in Fuzzy Normed Spaces"}

We establish some stability results concerning the general cubic functional equationf(x + ky) - kf(x + y) + kf(x - y) - f(x - ky) = 2k(k2 - 1)f(y)for fixed k...

Stability of General Cubic Mapping in Fuzzy Normed Spaces

Published Online: May 17, 2013

Page range: 129 - 150

DOI: https://doi.org/10.2478/v10309-012-0010-y

Keywords
Generalized Hyers-Ulam-Rassias stability, Cubic functional equation, Fuzzy normed spaces

This content is open access.

Stability of General Cubic Mapping in Fuzzy Normed Spaces

Published Online: May 17, 2013

Page range: 129 - 150

DOI: https://doi.org/10.2478/v10309-012-0010-y

KeywordsGeneralized Hyers-Ulam-Rassias stability, Cubic functional equation, Fuzzy normed spaces

This content is open access.

Keywords
Generalized Hyers-Ulam-Rassias stability, Cubic functional equation, Fuzzy normed spaces