• The Pure and Applied Mathematics
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• v.16 no.2
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• pp.227-241
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• 2009

Let A be a Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A $\rightarrow$ A such that $[D(x),\;x]D(x)^2[D(x),\;x]\;{\in}\;rad(A)$ for all $x\;{\in}\;A$. Then we have D(A) $\subseteq$ rad(A).

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.259-296
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• 2008

Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A $\rightarrow$ A such that $D(x)^2$[D(x),x] $\in$ rad(A) or [D(x),x]$D(x)^2$ $\in$ rad(A) for all x $\in$ A. In this case, we have D(A) $\subseteq$ rad(A).

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.179-201
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• 2008

Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation $D\;:\;A{\rightarrow}A$ such that $D(x)[D(x),x]^2\;{\in}\;rad(A)$ or $[D(x), x]^2 D(x)\;{\in}\;rad(A)$ for all $x\;{\in}\ A$. In this case, we have $D(A)\;{\subseteq}\;rad(A)$.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.811-818
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• 2019

Let A be a Banach algebra with rad(A). We show that if there exists a continuous linear Jordan derivation D on A, then $$[D(x),x]D(x)^2{\in}rad(A)$$ if and only if $D(x)[D(x),x]D(x){\in}rad(A)$ for all $x{\in}A$.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.269-287
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• 2021

In this paper, we prove some coupled fixed point theorems satisfying some generalized contractive condition in a cone metric space over a Banach algebra. We also applied the results obtained to show coupled fixed point of some contractive mapping of integral type.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.809-823
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• 2020

Let C[0, T] denote the space of continuous, real-valued functions on the interval [0, T] and let C₀[0, T] be the space of functions x in C[0, T] with x(0) = 0. In this paper, we introduce a Banach algebra ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ on C[0, T] and its equivalent space ${\bar{\mathcal{F}}}({\mathcal{H}}) $, a space of transforms of equivalence classes of measures, which generalizes Fresnel class 𝓕(𝓗), where 𝓗 is an appropriate real separable Hilbert space of functions on [0, T]. We also investigate their properties and derive an isomorphism between ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ and ${\bar{\mathcal{F}}}({\mathcal{H}}) $. When C[0, T] is replaced by C₀[0, T], ${\bar{\mathcal{F}}}({\mathcal{H}}) $ and ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ reduce to 𝓕(𝓗) and Cameron-Storvick's Banach algebra 𝓢, respectively, which is the space of generalized Fourier-Stieltjes transforms of the complex-valued, finite Borel measures on L²[0, T].

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.467-474
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• 2004

We prove the generalized Hyers-Ulam-Rassias stability of a partitioned functional equation. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with partitioned functional equations in Banach algebras.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.937-942
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• 1999

In this paper we will show that if [G($\chi$),$\chi$] D($\chi$) and [D($\chi$), G($\chi$)] lie in the nil radical of A for all $\chi$$\in$A, then either D or G maps A into the radical where D and G are derivations on a Banach algebra A.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.497-504
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• 2020

A weight ω on the positive half real line [0, ∞) is a positive continuous function such that ω(s + t) ≤ ω(s)ω(t), for all s, t ∈ [0, ∞), and ω(0) = 1. The weighted convolution Banach algebra L1(ω) is the algebra of all equivalence classes of Lebesgue measurable functions f such that ‖f‖ = ∫0∞|f(t)|ω(t)dt < ∞, under pointwise addition, scalar multiplication of functions, and the convolution product (f ⁎ g)(t) = ∫0t f(t - s)g(s)ds. We give a sufficient condition on a weight function ω(t) in order that L1(ω) has a bounded approximate identity.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.259-267
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• 2002

Let X be a hemicompact space with ($K_{n}$) as an admissible exhaustion, and for each n $\in$ N, $A_{n}$ a Banach function algebra on $K_{n}$ with respect to $\parallel.\parallel_n$ such that $A_{n+1}\midK_{n}$$\subsetA_n$ and${\parallel}f{\mid}K_n{\parallel}_n{\leq}{\parallel}f{\parallel}_{n+1}$ for all f$\in$$A_{n+1}$, We consider the subalgebra A = { f $\in$ C(X) : $\forall_n\;{\epsilon}\;\mathbb{N}$ of C(X) as a frechet function algebra and give a result related to its spectrum when each $A_{n}$ is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.