Homomorphism-derivation functional inequalities in C*-algebrasopen access
- Authors
- Park, Choonkil; Wu, XiaoYing
- Issue Date
- 2020
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- Keywords
- additive-additive (s, t)-functional inequality; derivation and homomorphism in C*-ternary algebra; derivation and homomorphism in unital C*-algebra
- Citation
- AIMS MATHEMATICS, v.5, no.5, pp.4482 - 4493
- Indexed
- SCIE
SCOPUS
- Journal Title
- AIMS MATHEMATICS
- Volume
- 5
- Number
- 5
- Start Page
- 4482
- End Page
- 4493
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/146511
- DOI
- 10.3934/math.2020288
- ISSN
- 2473-6988
- Abstract
- In this paper, we introduce and solve the following additive-additive (s, t)-functional inequality
parallel to g (x + y) - g(x) - g(y)parallel to + parallel to 2h(x+y/2) - h(x) - h(y)parallel to (0,1)
<= parallel to s(2g(x+y/2) - g(x) - g(y)parallel to + parallel to t(h(x=y) - h(x) - h(y))parallel to,
where s and t are fixed nonzero complex numbers with vertical bar s vertical bar < 1 and vertical bar t vertical bar < 1. Furthermore, we investigate homomorphisms and derivations in complex Banach algebras and unital C*-algebras, associated to the additive-additive (s, t)-functional inequality (0.1) under some extra condition.
Moreover, we introduce and solve the following additive-additive (s, t)-functional inequality
parallel to g (x + y + z) - g(x) - g(y) g(z)parallel to + parallel to 3h (x + y +z/3) + h(x -2y + z) + h(x + y -2z) - 3h(x)parallel to
<= parallel to s(3g(x+y+z/3) - g(x) - g(y) - g(z)parallel to (0,2)
+ parallel to t (h(x +y +z) + h(x - 2y + z) + h(x + y -2z) -3h(x))parallel to.
where s and t are fixed nonzero complex numbers with vertical bar s vertical bar < 1 and vertical bar t vertical bar < 1. Furthermore, we investigate C*-ternary derivations and C*-ternary homomorphisms in C*-ternary algebras, associated to the additive-additive (s, t)-functional inequality (0.2) under some extra condition.
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