Author:
Selvan Arumugam Ponmana,Najati Abbas
Abstract
AbstractThe main aim of this paper is to establish the Hyers–Ulam stability and hyperstability of a Jensen-type quadratic mapping in 2-Banach spaces. That is, we prove the various types of Hyers–Ulam stability and hyperstability of the Jensen-type quadratic functional equation of the form $$ g \biggl( \frac{x+y}{2} + z \biggr) + g \biggl( \frac{x+y}{2} - z \biggr) + g \biggl( \frac{x-y}{2} + z \biggr) + g \biggl( \frac{x-y}{2} - z \biggr) = g(x) + g(y) + 4 g(z), $$
g
(
x
+
y
2
+
z
)
+
g
(
x
+
y
2
−
z
)
+
g
(
x
−
y
2
+
z
)
+
g
(
x
−
y
2
−
z
)
=
g
(
x
)
+
g
(
y
)
+
4
g
(
z
)
,
in 2-Banach spaces by using the Hyers direct method.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference23 articles.
1. Aoki, T.: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. 2, 64–66 (1950)
2. Bae, J.H., Noori, B., Moghimi, M.B., Najati, A.: Inner product spaces and quadratic functional equations. Adv. Differ. Equ. 2021, 139 (2021)
3. Cholewa, P.W.: Remarks on the stability of functional equations. Aequ. Math. 27, 76–86 (1984)
4. Czerwik, S.: On the stability of the quadratic mapping in normed spaces. Abh. Math. Semin. Univ. Hamb. 62, 59–64 (1992)
5. Day, M.M.: Some characterizations of inner-product spaces. Trans. Am. Math. Soc. 62, 320–337 (1947)
Cited by
11 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献