Journal
JOURNAL OF MATHEMATICAL INEQUALITIES
Volume 9, Issue 2, Pages 397-407Publisher
ELEMENT
DOI: 10.7153/jmi-09-33
Keywords
Hyers-Ulam stability; additive rho-functional equation; additive rho-functional inequality; non-Archimedean normed space
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Funding
- Basic Science Research Program through the National Research Foundation of Korea - Ministry of Education, Science and Technology [NRF-2012R1A1A2004299]
- National Research Foundation of Korea [2012R1A1A2004299] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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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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