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CAUCHY-RASSIAS STABILITY OF CAUCHY-JENSEN ADDITIVE MAPPINGS IN BANACH SPACES
Cauchy additive mapping Jensen additive mapping Cauchy--Rassias stability isomorphism between Banach algebra
2007/12/11
Let $X, Y$ be vector spaces. It is shown that if a mapping $f : X \rightarrow Y$ satisfies $$\align &f\bigg(\frac{x+y}{2}+z\bigg) + f\bigg(\frac{x-y}{2}+z\bigg) = f(x)+2f(z) , \tag 0.1 \&f\bigg(\frac{...