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

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
332
Issue
2
Identifiers
DOI: 10.1016/j.jmaa.2006.11.024
Keywords
  • Hyers–Ulam–Rassias Stability
  • Functional Inequality
  • Cubic Mapping
  • Quasi-Banach Spaces
  • P-Banach Spaces

Abstract

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.

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