Stability of General Cubic Mapping in Fuzzy Normed Spaces

S. Javadi; J. M. Rassias

doi:10.2478/v10309-012-0010-y

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Stability of General Cubic Mapping in Fuzzy Normed Spaces

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 20 (2012): Issue 1 (May 2012)

By: S. Javadi and J. M. Rassias

Open Access

|May 2013

Abstract

We establish some stability results concerning the general cubic functional equation

f(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

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