ADDITIVE ρ-FUNCTIONAL EQUATIONS IN NON-ARCHIMEDEAN BANACH SPACE
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In this paper, we solve the additive ρ-functional equations (0.1) f(x + y) + f(x - y) - 2f(x) = ρ(2f(x + y)/2) + f(x - y) - 2f(x)), where ρ is a fixed non-Archimedean number with |ρ| < 1, and (0.2) 2f(x + y)/2) + f(x - y) - 2f(x) = ρ(f(x + y) + f(x - y) - 2f(x)), where ρ is a fixed non-Archimedean number with |ρ| < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive ρ-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.
Abstract
In this paper, we solve the additive ρ-functional equations (0.1) f(x + y) + f(x - y) - 2f(x) = ρ(2f(x + y)/2) + f(x - y) - 2f(x)), where ρ is a fixed non-Archimedean number with |ρ| < 1, and (0.2) 2f(x + y)/2) + f(x - y) - 2f(x) = ρ(f(x + y) + f(x - y) - 2f(x)), where ρ is a fixed non-Archimedean number with |ρ| < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive ρ-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.
참고문헌 (10)
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