Abstract
This paper introduces a new dimension of an additive functional equation and obtains its general solution. The main goal of this study is to examine the Ulam stability of this equation in IFN-spaces (intuitionistic fuzzy normed spaces) with the help of direct and fixed point approaches and 2-Banach spaces. Also, we use an appropriate counterexample to demonstrate that the stability of this equation fails in a particular case.
Highlights
For all x ∈ G? Ulam defined such a problem in 1940 and solved it the following year for the Cauchy functional equation ψ(u + v) ψ(u) + ψ(v)
Nakmahachalasint [6] gave the overall answer and HUR stability of finite variable functional equation; Khodaei and Rassias [7] examined the stability of generalized additive functions in several variables. e stability result of additive functional equations was examined by means of Najati and Moghimi [8], Shin et al [9], and Gordji [10]
We present a new kind of additive functional equation: s
Summary
If a mapping φ between two real vector spaces W and F satisfies functional equation (4), the function φ is additive. Vs) by (v, v, 0√,√0√√, ..√.√,√√0) in (4), we have (s− 2)− times φ(2v) 2φ(v),. For any non-negative integer a > 0, we have φ 2av 2aφ(v),. Vs) by (s, t, 0√,√0√√, ..√.√,√√0) in (4), we obtain (3) for all s, t ∈ W. If a mapping φ between two real vector spaces W and F satisfies functional equation (3), the function φ satisfies additive functional equation (4), for all v1, v2, v3, . S 1≤a
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