Hyers-Ulam stability of an additive-quadratic functional equationopen access
- Authors
- Govindan, Vediyappan; Park, Choonkil; Pinelas, Sandra; Rassias, Themistocles M.
- Issue Date
- Aug-2020
- Publisher
- Universidad de la Frontera
- Keywords
- Hyers-Ulam stability; mixed type functional equation; Banach space; fixed point
- Citation
- Cubo, v.22, no.2, pp.233 - 255
- Indexed
- SCOPUS
- Journal Title
- Cubo
- Volume
- 22
- Number
- 2
- Start Page
- 233
- End Page
- 255
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/145342
- DOI
- 10.4067/S0719-06462020000200233
- ISSN
- 0716-7776
- Abstract
- In this paper, we introduce the following (a, b, c)-mixed type functional equation of the form g(ax1 + bx2 + cx3) − g(−ax1 + bx2 + cx3) + g(ax1 − bx2 + cx3) − g(ax1 + bx2 − cx3) + 2a2 [g(x1) + g(−x1)] + 2b2 [g(x2) + g(−x2)] + 2c2 [g(x3) + g(−x3)] + a[g(x1) − g(−x1)] + b[g(x2) − g(−x2)] + c[g(x3) − g(−x3)] = 4g(ax1 + cx3) + 2g(−bx2) + 2g(bx2) where a, b, c are positive integers with a > 1, and investigate the solution and the Hyers-Ulam stability of the above functional equation in Banach spaces by using two different methods.
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