On the stability of Euler–Lagrange type cubic mappings in quasi-Banach spaces

By K. Jun, Hark-Mahn Kim. 2007

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Abstract In this paper, we solve the generalized Hyers–Ulam–Rassias stability problem for Euler–Lagrange type cubic functional equations f ( a x + y ) + f ( x + a y ) = ( a + 1 ) ( a − 1 ) 2 [ f ( x ) + f ( y ) ] + a ( a + 1 ) f ( x + y ) for mappings f : X → Y in quasi-Banach spaces and for fixed integers a with a ≠ 0 , ± 1 . In addition, we also present a counterexample that does not satisfy the stability based on Ulam's question.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/28bfa013e09b73cc13e4531961122be880fe23ac