Several stability problems of a quadratic functional equation
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In this paper, we investigate the stability using shadowing property in Abelian metric group and the generalized Hyers-Ulam-Rassias stability in Banach spaces of a quadratic functional equation, f(x_1+x_2+x_3+x_4)+f(-x_1+x_2-x_3+x_4)+f(-x_1+x_2+x_3)+f(-x_2+x_3+x_4)+f(-x_3+x_4+x_1)+f(-x_4+x_1+x_2)=5(기호)f(x_i). Also, we study the stability using the alternative fixed point theory of the functional equation in Banach spaces.
Abstract
In this paper, we investigate the stability using shadowing property in Abelian metric group and the generalized Hyers-Ulam-Rassias stability in Banach spaces of a quadratic functional equation, f(x_1+x_2+x_3+x_4)+f(-x_1+x_2-x_3+x_4)+f(-x_1+x_2+x_3)+f(-x_2+x_3+x_4)+f(-x_3+x_4+x_1)+f(-x_4+x_1+x_2)=5(기호)f(x_i). Also, we study the stability using the alternative fixed point theory of the functional equation in Banach spaces.
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