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Orthogonally additive and orthogonally quadratic functional equation

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강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2013.03|한국수학논문집 (Korean Journal of Mathematics)|제21권 제1호|pp. 1-21|DOI http://dx.doi.org/10.11568/kjm.2013.21.1.1

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참고문헌

키워드

fixed pointUlam-Hyers stabilityorthogonality spacenon-Archimedean normed space
주제분류수학

초록

Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation f(x/2+y)+f(x/2−y)+f(x/2+z)+f(x/2−z)(0.1)=3/2f(x)−1/2f(−x)+f(y)+f(−y)+f(z)+f(−z) for all x, y, z with x ⊥ y, in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

Abstract

Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation f(x/2+y)+f(x/2−y)+f(x/2+z)+f(x/2−z)(0.1)=3/2f(x)−1/2f(−x)+f(y)+f(−y)+f(z)+f(−z) for all x, y, z with x ⊥ y, in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

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