Journal
AIMS MATHEMATICS
Volume 7, Issue 6, Pages 10700-10710Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2022597
Keywords
Hyers-Ulam stability; 3-additive functional equation; hyper derivation; hyper homomrphism; 3-linear mapping
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This paper introduces the concepts of hyper homomorphisms and hyper derivations in Banach algebras, and establishes their stability in a specific functional equation.
In this paper, we introduce the concept of hyper homomorphisms and hyper derivations in Banach algebras and we establish the stability of hyper homomorphisms and hyper derivations in Banach algebras for the following 3-additive functional equation: g(x(1) + x(2), y(1) + y(2),z(1) + z(2)) = Sigma(2)(i,j,k=1) g(x(i), y(j), z(k)).
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