Stability and Superstability of Generalized ( 𠜃, 𠜙 )-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation

M. Eshaghi Gordji, M. B. Ghaemi, G. H. Kim and Badrkhan Alizadeh

Journal of Applied Mathematics, 2011, vol. 2011, 1-11

Abstract:

Let ð ´ be an algebra, and let 𠜃 , 𠜙 be ring automorphisms of ð ´ . An additive mapping ð » âˆ¶ ð ´ â†’ ð ´ is called a ( 𠜃 , 𠜙 ) -derivation if ð » ( ð ‘¥ 𠑦 ) = ð » ( ð ‘¥ ) 𠜃 ( 𠑦 ) + 𠜙 ( ð ‘¥ ) ð » ( 𠑦 ) for all ð ‘¥ , 𠑦 ∈ ð ´ . Moreover, an additive mapping ð ¹ âˆ¶ ð ´ â†’ ð ´ is said to be a generalized ( 𠜃 , 𠜙 ) -derivation if there exists a ( 𠜃 , 𠜙 ) -derivation ð » âˆ¶ ð ´ â†’ ð ´ such that ð ¹ ( ð ‘¥ 𠑦 ) = ð ¹ ( ð ‘¥ ) 𠜃 ( 𠑦 ) + 𠜙 ( ð ‘¥ ) ð » ( 𠑦 ) for all ð ‘¥ , 𠑦 ∈ ð ´ . In this paper, we investigate the superstability of generalized ( 𠜃 , 𠜙 ) -derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy’s functional equation.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:726020

DOI: 10.1155/2011/726020

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