Abstract
Rassias(2001) introduced the pioneering cubic functional equation in the history of mathematical analysis: and solved the pertinent famous Ulam stability problem for this inspiring equation. This Rassias cubic functional equation was the historic transition from the following famous Euler-Lagrange-Rassias quadratic functional equation: to the cubic functional equations. In this paper, we prove the Ulam-Hyers stability of the cubic functional equation: in fuzzy normed linear spaces. We use the definition of fuzzy normed linear spaces to establish a fuzzy version of a generalized Hyers-Ulam-Rassias stability for above equation in the fuzzy normed linear space setting. The fuzzy sequentially continuity of the cubic mappings is discussed.
Highlights
Studies on fuzzy normed linear spaces are relatively recent in the field of fuzzy functional analysis
Bag and Samanta 5 introduced a notion of boundedness of a linear operator between fuzzy normed spaces, and studied the relation between fuzzy continuity and fuzzy boundedness
The stability problem for the cubic functional equation was proved by Wiwatwanich and Nakmahachalasint 49 for mapping f : E1 → E2, where E1 and E2 are real Banach spaces
Summary
Studies on fuzzy normed linear spaces are relatively recent in the field of fuzzy functional analysis. In 1984, Katsaras 1 first introduced a definition of fuzzy norm on a linear space. M. Rassias 10 gave a further generalization of the result of Hyers and prove the following theorem using weaker conditions controlled by a product of powers of norms.
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