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ADDITIVE rho-FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN NORMED SPACES
- Authors
- Park, Choonkil
- Issue Date
- Jun-2015
- Publisher
- Element d.o.o.
- Keywords
- Hyers-Ulam stability; additive rho-functional equation; additive rho-functional inequality; non-Archimedean normed space
- Citation
- Journal of Mathematical Inequalities, v.9, no.2, pp 397 - 407
- Pages
- 11
- Indexed
- SCIE
SCOPUS
- Journal Title
- Journal of Mathematical Inequalities
- Volume
- 9
- Number
- 2
- Start Page
- 397
- End Page
- 407
- ISSN
- 1846-579X
- 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. Furthermore, we prove the Hyers-Ulam stability of the additive rho-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of additive rho-functional equations associated with the additive rho-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.
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