Abstract
Abstract Using fixed point method, we establish the Hyers-Ulam stability of m-Lie homomorphisms and Jordan m-Lie homomorphisms in m-Lie algebras associated to the following generalized Jensen functional equation ∑ i = 1 m μ f ( x i ) = 1 2 m [ ∑ i = 1 m f ( μ m x i + ∑ j = 1 , i ≠ j m x j ) + f ( ∑ i = 1 m μ x i ) ] for a fixed positive integer m with m ≥ 2. Mathematics Subject Classification (2010): Primary 17A42, 39B82, 39B52.
Highlights
Let n be a natural number greater or equal to 3
For n = 3, this product is a special case of the Nambu bracket, well-known in physics, which was introduced by Nambu [2] in 1973, as a generalization of the Poisson bracket in Hamiltonian mechanics
By using fixed point method, we establish the Hyers-Ulam stability of n-Lie homomorphisms and Jordan n-Lie homomorphisms in n-Lie Banach algebras associated to the following generalized Jensen-type functional equation m i=1 μf (xi)
Summary
Let n be a natural number greater or equal to 3. A C -linear mapping H: (A, [ ]A) ® (B, [ ]B) is called an n-Lie homomorphism if
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