• Journal of the Chungcheong Mathematical Society
• /
• v.4 no.1
• /
• pp.49-54
• /
• 1991

In the paper of Johnson[4], the results about continuity of homomorphisms were applied to those of generalized homomorphisms. This paper presents the results helpful to prove the continuity of generalized homomorphisms on Banach algebra and the continuity of generalized homomorphisms on it.

• Honam Mathematical Journal
• /
• v.42 no.2
• /
• pp.411-423
• /
• 2020

In this paper, we correct some errors and typos of [2] and introduce a new concept related to pseudo n-Jordan homomorphisms, that we call it pseudo n-homomorphism. We investigate automatic continuity and positivity of pseudo n-homomorphisms and pseudo n-Jordan homomorphisms on Banach algebras and C*-algebras. Moreover, we show that the sum of two pseudo n-Jordan homomorphisms is not a pseudo n-Jordan homomorphism and we show that under some conditions the sum of two pseudo n-Jordan homomorphisms is a pseudo n-Jordan homomorphism.

• Honam Mathematical Journal
• /
• v.42 no.4
• /
• pp.757-768
• /
• 2020

In this paper, the Hyers-Ulam-Rassias stability of mixed n-Jordan homomorphisms on Banach algebras and the superstability of mixed n-Jordan ∗-homomorphism between C∗-algebras are investigated.

• Communications of the Korean Mathematical Society
• /
• v.13 no.2
• /
• pp.243-249
• /
• 1998

In this paper, we introduce a congruence relation on a semiring and a quotient semiring, and prove some homomorphism theorems.

• Kyungpook Mathematical Journal
• /
• v.23 no.1
• /
• pp.13-18
• /
• 1983

• The Pure and Applied Mathematics
• /
• v.26 no.4
• /
• pp.305-313
• /
• 2019

Using the fixed point method, we prove the Hyers-Ulam stability of 3-Lie homomorphisms and 3-Lie derivations in 3-Lie algebras for Cauchy-Jensen functional equation.

• The Pure and Applied Mathematics
• /
• v.24 no.3
• /
• pp.171-178
• /
• 2017

In this paper, we define $C^*-ternary$ quadratic 3-Jordan homomorphisms associated with the quadratic mapping f(x + y) + f(x - y) = 2f(x) + 2f(y), and prove the Hyers-Ulam stability of $C^*-ternary$ quadratic 3-Jordan homomorphisms.

• Communications of the Korean Mathematical Society
• /
• v.23 no.3
• /
• pp.453-459
• /
• 2008

We introduce a concept of continuous homomorphisms between Csaszar frames and show that the Cauchy completion in CsFrm gives rise to a coreflection in the category PCsFrm (resp. UCsFrm) consisting of proximal Csaszar frames and uniform continuous homomor-phisms (resp. uniform Csaszar frames and uniform continuous homomor-phisms).

• East Asian mathematical journal
• /
• v.30 no.3
• /
• pp.259-270
• /
• 2014

For a generalized triangular matrix ring $$T=\[\array{R\;M\\0\;S}]$$, over rings R and S having only the idempotents 0 and 1 and over an (R, S)-bimodule M, we characterize all homomorphisms ${\alpha}$'s and all ${\alpha}$-derivations of T. Some of the homomorphisms are compositions of an inner homomorphism and an extended or a twisted homomorphism.

• Honam Mathematical Journal
• /
• v.43 no.1
• /
• pp.68-77
• /
• 2021

This paper considers pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. We characterize pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. Moreover, we define pseudo derivations on the above stated Banach algebras and characterize this new notion on those algebras.