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Additive ρ-functional inequalities in non-archimedean 2-normed spaces
- Authors
- Wang, Z.; Park, C.; Shin, D.Y.
- Issue Date
- 2021
- Publisher
- American Institute of Mathematical Sciences
- Keywords
- additive ρ-functional equation; additive ρ-functional inequality; Hyers-Ulam stability; non-Archimedean 2-normed spaces
- Citation
- AIMS Mathematics, v.6, no.2, pp.1905 - 1919
- Indexed
- SCIE
SCOPUS
- Journal Title
- AIMS Mathematics
- Volume
- 6
- Number
- 2
- Start Page
- 1905
- End Page
- 1919
- ISSN
- 2473-6988
- Abstract
- In this paper, we solve the additive rho-functional inequalities: parallel to f (x + y) - f(x) - f(y)parallel to <= parallel to rho(2f(x + y/2) - f(x) - f(y))parallel to, parallel to 2f (x + y/2) - f(x) - f(y)parallel to <= parallel to rho(f(x + y) - f(x) - f(y))parallel to, where rho is a fixed non-Archimedean number with vertical bar rho vertical bar < 1. More precisely, we investigate the solutions of these inequalities in non-Archimedean 2-normed spaces, and prove the Hyers-Ulam stability of these inequalities in non-Archimedean 2-normed spaces. Furthermore, we also prove the Hyers-Ulam stability of additive rho-functional equations associated with these inequalities in non-Archimedean 2-normed spaces.
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