• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.959-967
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• 2011

Let A be a Banach algebra and let f : $A{\times}A{\rightarrow}A$ be an approximate bi-derivation in the sense of Hyers-Ulam-Rassias. In this note, we proves the Hyers-Ulam-Rassias stability of bi-derivations on Banach algebras. If, in addition, A is unital, then f : $A{\times}A{\rightarrow}A$ is an exact bi-derivation. Moreover, if A is unital, prime and f is symmetric, then f = 0.

• Transactions on Electrical and Electronic Materials
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• v.2 no.1
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• pp.12-15
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• 2001

Bi-2212 and Bi-2223 thin films are prepared by IBS(ion beam sputtering) technique. Three phases of Bi-2201, Bi-2212 and Bi-2223 appear as stable ones in spite of the conditions for thin film fabrication of Bi-2212 and Bi-2223 compositions, depending on substrate temperature (T $_{sub}$) and ozone pressure(PO$_3$). It is found out that these phases are limited within very narrow temperature.e.

• The Pure and Applied Mathematics
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• v.17 no.3
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• pp.231-247
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• 2010

In this paper, we investigate the generalized Hyers-Ulam stability of a bi-Jensen functional equation $4f(\frac{x\;+\;y}{2},\;\frac{z\;+\;w}{2})$ = f(x, z) + f(x, w) + f(y, z) + f(y, w). Also, we establish improved results for the stability of a bi-Jensen equation on the punctured domain.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.383-398
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• 2009

In this paper, we study the generalized Hyers-Ulam stability of a bi-Jensen functional equation $$4f(\frac{x+y}{2},\;\frac{z+w}{2})=f(x,\;z)+f(x,w)+f(y,\;z)+f(y,w)$$. Moreover, we establish stability results on the punctured domain.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.335-348
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• 2010

In this paper, we study the Hyers-Ulam-Rassias stability of a bi-Pexider functional equation $$f(x+y,z)-f_1(x,z)-f_2(y,z)=0$$, $$f(x,y+z)-f_3(x,y)-f_4(x,z)=0$$. Moreover, we establish stability results on the punctured domain.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.161-170
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• 2013

Bae and W. Park [3] proved the Hyers-Ulam stability of bi-homomorphisms and bi-derivations in $C^*$-ternary algebras. It is easy to show that the definitions of bi-homomorphisms and bi-derivations, given in [3], are meaningless. So we correct the definitions of bi-homomorphisms and bi-derivations. Under the conditions in the main theorems, we can show that the related mappings must be zero. In this paper, we correct the statements and the proofs of the results, and prove the corrected theorems.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2000.11a
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• pp.108-111
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• 2000

Bi2212 and Bi2223 thin films are fabricated by ion beam sputtering method. Three phases of Bi2201, Bi2212 and Bi2223 appear as stable ones in spite of the condition for thin film fabrication of Bi2212 and bi2223 compositions, depending on substrate temperature(T$\sub$sub/) and ozone pressure (PO$_3$). It is found out that these phases show similar T$\sub$sub/ and PO$_3$dependence, and that the stable regions of these phases are limited within very narrow temperature.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.11b
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• pp.308-311
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• 2001

Bi-2212 and Bi-2223 thin films are prepared by IBS(ion beam sputtering) technique. Three phases of Bi-2201, Bi-2212 and Bi-2223 appear as stable ones in spite of the conditions for thin film fabrication of Bi-2212 and Bi-2223 compositions, depending on substrate temperature($T_{sub}$) and ozone pressure( $PO_3$ ). It is found out that these phases show similar $T_{sub}$ and $PO_3$ dependence, and that the stable regions of these phases are limited within very narrow temperature.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.11a
• /
• pp.308-311
• /
• 2001

Bi-2212 and Bi-2223 thin films are prepared by IBS(ion beam sputtering) technique. Three phases of Bi-2201, Bi-2212 and Bi-2223 appear as stable ones in spite of the conditions for thin film fabrication of Bi-2212 and Bi-2223 compositions, depending on substrate temperature($T_{sub}$) and ozone pressure(PO$_3$). It is found out that these phases show similar $T_{sub}$ and PO$_3$ dependence, and that the stable regions of these phases are limited within very narrow temperature.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2000.11a
• /
• pp.108-111
• /
• 2000

Bi2212 and Bi2223 thin films are fabricated by ion beam sputtering method. Three phases of Bi2201, Bi2212 and Bi2223 appear as stable ones in spite of the condition for thin film fabrication of Bi2212 and bi2223 compositions, depending on substrate temperature(T$\sub$sub/) and ozone pressure (PO$_3$). It is found out that these phases show similar T$\sub$sub/ and PO$_3$ dependence, and that the stable regions of these phases are limited within very narrow temperature.