Ulam stability of an additive-quadratic functional equation in Banach spaces

Hwang, In-Ho; Park, Choonkil

doi:10.7153/jmi-2020-14-27

Cited by 13 publications

(9 citation statements)

References 10 publications

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“…Theorem 8 with n = 2, a 1,1,1 = a 2,1,1 = a 1,−1,−1 = a 2,−1,−1 = 1, a 1,1,−1 = a 2,1,−1 = a 1,−1,1 = a 2,−1,1 = 0, A 1,1 = A 1,2 = 2 and A 2,1 = A 2,2 = 0 gives also the following outcomes on the Ulam stability of functional equation ( 27) (let us mention that the stability of this equation was very recently studied in [35]).…”

Section: Corollary 9 Assume That Y Is a Banach Space And ϕmentioning

confidence: 89%

On perturbations of two general equations in several variables

Ciepliński

2022

Math. Ann.

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In this paper, we deal with perturbations of two general functional equations in several variables. Namely, we prove the generalized, in the spirit of Bourgin, Ulam stability of these equations in Banach spaces. In order to do this, we use the fixed point method. Moreover, as corollaries from our main results, we get several outcomes on approximate solutions of a few important classic equations. They include, among others, the functional equations which characterize multi-additive and multi-quadratic mappings. In consequence, the perturbation of homomorphisms of Banach spaces and quadratic mappings is also treated.

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Section: Corollary 9 Assume That Y Is a Banach Space And ϕmentioning

confidence: 89%

On perturbations of two general equations in several variables

Ciepliński

2022

Math. Ann.

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“…Finally, we derive from Theorem 4 the Ulam stability of the functional equations (let us mention that the stability of Eq. (20) in Banach spaces was very recently studied in [31], whereas Eq. ( 21) was introduced and studied in [41]).…”

Section: Some Consequencesmentioning

confidence: 99%

Ulam stability of functional equations in 2-Banach spaces via the fixed point method

Ciepliński

2021

J. Fixed Point Theory Appl.

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Using the fixed point method, we prove the Ulam stability of two general functional equations in several variables in 2-Banach spaces. As corollaries from our main results, some outcomes on the stability of a few known equations being special cases of the considered ones will be presented. In particular, we extend several recent results on the Ulam stability of functional equations in 2-Banach spaces.

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“…Let us mention here that assumption (4) is natural in stability considerations on some types of functional equations, and it also appears in particular cases of (1) (see for instance [11,21,28]). Whether it can be omitted is an open question.…”

Section: Therefore D(t G T H) ≤ Lc Gh and Consequently D(t G T H) ≤ Ld(g H)mentioning

confidence: 99%

“…Now, we present some further consequences of Theorem 2. Namely, we apply it to get some Hyers-Ulam stability results for three functional equations studied in [21,28,29]. These equations are connected with the two famous functional equations:…”

Section: Some Consequencesmentioning

confidence: 99%