2017•JOURNAL OF ADVANCES IN PHYSICSOpen access

On The Stability Problem of Quadratic Functional Equations in 2-Banach Spaces

Seong-Sik Kim, Ga Ya Kim, Soo Hwan Kim

Abstract

In this paper, we investigate the stability problem in the spirit of Hyers-Ulam, Rassias and Gavruta for the quadratic functional equation: f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 4f(x) - 2f(y) in 2-Banach spaces. These results extend the generalized Hyers-Ulam stability results by the quadratic functional equation in normed spaces to 2-Banach spaces.

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Key concepts: Banach space, Quadratic equation, Stability (learning theory), Functional analysis, Pure mathematics, Mathematics, Mathematical analysis, Applied mathematics