A fixed point approach to the stability of an AQ-functional equation on β-Banach modules

Using the fixed point method, we prove the Hyers-Ulam stability of the following mixed additive and quadratic functional equation f ( kx + y ) + f ( kx - y ) = f ( x + y ) + f ( x - y ) + ( k - 1) [( k + 2) f ( x ) + kf (- x )] ( k ∈ ℕ, k ≠ 1) in β -Banach modules on a Banach algebra. MR(2000) Subje...

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Bibliographic Details
Published inFixed point theory and applications (Hindawi Publishing Corporation) Vol. 2012; no. 1; pp. 1 - 14
Main Authors Xu, Tian Zhou, Rassias, John Michael
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2012
Subjects
Additives
Algebra
Analysis
Applications of Mathematics
Classification
Differential Geometry
Fixed points (mathematics)
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Modules
Stability
Topology
Banach module
fixed point method
AQ-functional equation
Hyers-Ulam stability
generalized metric space
unital Banach algebra
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ISSN1687-1812
1687-1820
1687-1812
DOI10.1186/1687-1812-2012-32

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Summary:Using the fixed point method, we prove the Hyers-Ulam stability of the following mixed additive and quadratic functional equation f ( kx + y ) + f ( kx - y ) = f ( x + y ) + f ( x - y ) + ( k - 1) [( k + 2) f ( x ) + kf (- x )] ( k ∈ ℕ, k ≠ 1) in β -Banach modules on a Banach algebra. MR(2000) Subject Classification . 39B82; 39B52; 46H25.
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ISSN:1687-1812
1687-1820
1687-1812
DOI:10.1186/1687-1812-2012-32