• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.245-252
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• 2002

In this paper we obtain some results concerning Jordan derivations and Jordan left derivations mapping into the Jacobson radical. Our main result is the following : Let d be a Jordan derivation (resp. Jordan left derivation) of a complex Banach algebra A. If d$^2$(x) = 0 for all x $\in$ A, then we have d(A) ⊆ red(A)

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.91-102
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• 2021

In this paper, we introduce Lie bracket Jordan derivations in Banach Jordan algebras. Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of Lie bracket Jordan derivations in complex Banach Jordan algebras.

• Asian Pacific Journal of Cancer Prevention
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• v.14 no.6
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• pp.3527-3534
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• 2013

Background: Cancer is a major health problem facing the entire world, and Jordan is no exception. However, patterns of cancer incidence and cancer burden in Jordan have never been explored thoroughly, and the aim of this study was to close this knowldege gap. Materials and Methods: The study was based on data obtained from the Jordan cancer registry from 1996 to 2009. All cancer cases that were diagnosed during the study period were registered and included in this study. Results: A total of 51,626 cases were registered in Jordan during the 14- year period. The incidence rate showed no significant increase in males (percent change PC 6.8%), while in females a marked increase was observed (PC 14.8%). The major cancer sites for males were bronchus and lung, colorectal, bladder, leukemia and prostate. In females, the leading cancer sites were breast, colorectal, leukemia, thyroid and NHL. Conclusions: Compared to other countries in the region, Jordan has comparable rates. On the other hand the rates of cancer are markedly lower in Jordan compared to more industrialized countries such as the US and Europe. There was an overall increase in the incidence of cancer in Jordan, especially among females, which stresses the need for programs to raise awareness on the importance of early diagnosis and preventive life style measures.

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

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.737-744
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• 2021

In this paper, among other things, we show that under special hypotheses every [pseudo] (n + 1)-Jordan homomorphism is a [pseudo] n-Jordan homomorphism and vice versa.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.69-73
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• 1997

We show that if T is an $\varepsilon$-approximate Jordan functional such that T(a) = 0 implies $T(a^2) = 0 (a \in A)$ then T is continuous and $\Vert T \Vert \leq 1 + \varepsilon$. Also we prove that every $\varepsilon$-near Jordan mapping is an $g(\varepsilon)$-approximate Jordan mapping where $g(\varepsilon) \to 0$ as $\varepsilon \to 0$ and for every $\varepsilon > 0$ there is an integer m such that if T is an $\frac {\varepsilon}{m}$-approximate Jordan mapping on a finite dimensional Banach algebra then T is an $\varepsilon$-near Jordan mapping.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.1-11
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• 2024

In this paper, we introduce the notion of 𝜎-Jordan amenability of Banach algebras and some hereditary are investigated. Similar to Johnson's classic result, we give the notions of 𝜎-Jordan approximate and 𝜎-Jordan virtual diagonals, and find some relations between the existence of them and 𝜎-Jordan amenability.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.505-517
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• 2014

We prove that every Jordan higher left (right) centralizer on a 2-torsion free semiprime ring is a higher left (right) centralizer which is to generalize the result of Zalar [18].

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

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.13-20
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• 2024

Let R be a ring with involution. In the present paper, we characterize biadditive mappings which satisfies some functional identities related to symmetric Jordan (𝛼, 1)^*-biderivation of prime rings with involution. In particular, we prove that on a 2-torsion free prime ring with involution, every symmetric Jordan triple (𝛼, 1)^*-biderivation is a symmetric Jordan (𝛼, 1)^*-biderivation.