Orthogonally Additive: Additive Functional Equation

Choonkil Park ()
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Choonkil Park: Hanyang University, Department of Mathematics

A chapter in Analytic Number Theory, Approximation Theory, and Special Functions, 2014, pp 759-772 from Springer

Abstract: Abstract Using fixed point method, we prove the Hyers–Ulam stability of the orthogonally additive–additive functional equation $$\displaystyle{f\left (\frac{x} {2} + y\right ) + f\left (\frac{x} {2} + z\right ) = f(x) + f(y) + f(z)}$$ for all x, y, z with x ⊥ y, in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

Keywords: Hyers Ulam Stability; Fixed Point Method; Birkhoff-James Orthogonality; Conditional Cauchy Functional Equation; Orthogonal Space (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-0258-3_29

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DOI: 10.1007/978-1-4939-0258-3_29

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