1. ADDITIVE ρ-FUNCTIONAL EQUATIONS.
- Author
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CHOONKIL PARK and SUN YOUNG JANG
- Subjects
- *
FUNCTIONAL equations , *REAL numbers , *REAL analysis (Mathematics) , *COMPLEX numbers , *BANACH spaces - Abstract
In this paper, we solve the additive ρ-functional equations f(x + y) - f(x) - f(y) = ρ(2f(x + y/2)-f(x)-f(y)), (0.1) 2f(x + y) - f(x) - f(y) = ρ (f(x + y) - f(x) - f(y)) ; (0.2) where ρ is a fixed non-Archimedean number or a fixed real or complex number with ρ≠1. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ- functional equations (0.1) and (0.2) in non-Archimedean Banach spaces and in Ba- nach spaces. [ABSTRACT FROM AUTHOR]
- Published
- 2017