Mohammad Sal Moslehian
In this paper, the generalized Hyers--Ulam--Rassias stability of $(σ-τ)$-derivations on normed algebras into Banach bimodules is established. We introduce the notion of approximate $(σ-τ)$-contractibility and prove that a Banach algebra is $(σ-τ)$-contractible if and only if it is approximately $(σ-τ)$-Contractible.
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In this paper the concepts of character contractibility, approximate character amenability (contractibility) and uniform approximate character amenability (contractibility) are introduced. We are concerned with the relations among the generalized concepts of character amenability for Banach algebra. We prove that approximate character amenability and approximate character contractibility are the same properties, as are uniform approximate character amenability and character amenability, as are uniform approximate character contractibility and character contractibility. For commutative Banach a…
We give a survey of our recent results on homological properties of K"othe algebras, with an emphasis on biprojectivity, biflatness, and homological dimension. Some new results on the approximate contractibility of K"othe algebras are also presented.
Hyers-Ulam-Rassias stability of functional equations with parameters
本文在β-齐次F-空间中研究广义Jensen加性和二次函数方程的Hyers-Ulam稳定性，证明近似映射存在唯一精确近似解。
In this paper, we study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space $X,$ the Lipschitz algebras $Lip_α(X)$ and $\ell ip_α(X)$ are approximately biflat if and only if $X$ is finite, provided that $0<α<1$. We give an enough and sufficient condition that a vector-valued Lipschitz algebras is Johnson pseudo-contractible for each $α>0.$ We also show that some triangular Banach algebras are not approximately biflat.
Given Banach algebras $ A $ and $ B $ with $ θ\inΔ(B) $. We shall study the Johnson pseudo-contractibility and pseudo-amenability of $ θ$-Lau product $ A\times_θ B $. We show that if $ A\times_θ B $ is Johnson pseudo-contractible, then $ A $ is Johnson pseudo-contractible and has a bounded approximate identity and $ B $ is Johnson pseudo-contractible. In some particular cases complete characterization of Johnson pseudo-contractibility of $ A\times_θ B $ are given. Also, we show that pseudo-amenability of $ A\times_θ B $ implies approximate amenability of $ A $ and pseudo-amenability of $ B $.
In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same properties. It is also shown that module uniform approximate (contractibility) amenability and module (contractibility, respectively) amenability for commutative Banach modules are equivalent. Applying t…
The aim of this article is to study a number of relationship between Frechet algebra $\mathcal{A}$ and its ultrapower $(\mathcal{A})_{\mathcal{U}}$. We give a characterization in some aspects such as locally bounded approximate identity. We consider the notion of contractibility of ultrapower of Frechet algebra, and we show that if $(\mathcal{A})_{\mathcal{U}}$ has approximation property with good ultrafilter $\mathcal{U}$ then $\mathcal{A}$ is contractible if and only if $(\mathcal{A})_{\mathcal{U}}$ is contractible.
We prove that an interesting result concerning generalized Hyers-Ulam-Rassias stability of a linear functional equation obtained in 2014 by S.M. Jung, D. Popa and M.T. Rassias in Journal of Global Optimization is a particular case of a fixed point theorem given by us in 2012. Moreover, we give a characterization of functions that can be approximated with a given error, by the solution of the previously mention linear equation.
We survey the recent investigations on (bounded, sequential) approximate amenability/contractibility and pseudo-amenability/contractibility for Banach algebras. We will discuss the core problems concerning these notions and address the significance of any solutions to them to the development of the field. A few new results are also included.
In this paper, we study the notion of $ϕ$-biflatness, $ϕ$-biprojectivity, approximate biprojectivity and Johnson pseudo-contractibility for a new class of Banach algebras. Using this class of Banach algebras we give some examples which are approximately biprojective. Also some Banach algebras are given among matrix algebras which are never Johnson pseudo-contractible.
In this paper, we establish the generalized Hyers--Ulam--Rassias stability of $C^*$-ternary ring homomorphisms associated to the Trif functional equation \begin{eqnarray*} d \cdot C_{d-2}^{l-2} f(\frac{x_1+... +x_d}{d})+ C_{d-2}^{l-1}\sum_{j=1}^d f(x_j) = l \cdot \sum_{1\leq j_1< ... < j_l\leq d} f(\frac{x_{j_1} + ... + x_{j_l}}{l}). \end{eqnarray*}
In this paper, we investigate the generalized Hyers--Ulam--Rassias stability of the system of functional equations $$f(xy)=f(x)f(y), \qquad\qquad. f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x), $$ on Banach algebras. Indeed we establish the superstability of above system by suitable control functions.
phi-semi contractible
本文引入Banach代数的phi-半可收缩性概念，给出其完整刻画，研究遗传性质，并证明射影张量积的等价条件，同时分析近似版本。
Stability of involutions on Banach Algebra by fixed point method
该研究采用Jensen函数方程稳定性的不动点方法，证明巴拿赫代数上对合的Hyers-Ulam-Rassias稳定性与超稳定性，还得到使带近似对合的巴拿赫代数成为$C^*$-代数的条件。
Let $A$ be a Banach ternary algebra over a scalar field $\Bbb R$ or $\Bbb C$ and $X$ be a ternary Banach $A-$module. Let $σ,τ$ and $ξ$ be linear mappings on $A$, a linear mapping $D:(A,[]_A)\to (X,[]_X)$ is called a Lie ternary $(σ,τ,ξ)-$derivation, if $$D([abc]_A)=[[D(a)bc]_X]_{(σ,τ,ξ)}+[[D(b)ac]_X]_{(σ,τ,ξ)}+[[D(c)ba]_X]_{(σ,τ,ξ)},$$ for all $a,b,c\in A$, where $[abc]_{(σ,τ,ξ)}=aτ(b)ξ(c)-σ(c)τ(b)a.$ In this paper, we investigate the generalized Hyers--Ulam--Rassias stability of Lie ternary $(σ,τ,ξ)-$derivations on Banach ternary algebras.
A mapping $f:(G_1,[ ]_1)\to (G_2,[ ]_2)$ between ternary semigroups will be called a ternary homomorphism if $f([xyz]_1)=[f(x)f(y)f(z)]_2$. In this paper, we prove the generalized Hyers--Ulam--Rassias stability of mappings of commutative semigroups into Banach spaces. In addition, we establish the superstability of ternary homomorphisms into Banach algebras endowed with multiplicative norms.
We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers--Ulam--Rassias stability of the quadratic functional equation $f(x+y)+f(x-y)=2f(x)+2f(y)$. Our result can be regarded as a generalization of the stability phenomenon in the framework of normed spaces. We also prove a generalized version of fuzzy stability of the Pexiderized quadratic functional equation $f(x+y)+f(x-y)=2g(x)+2h(y)$.
In this paper, we study the hereditary properties of module $(ϕ,φ)$-amenability on Banach algebras. We also define the concept of module character contractibility for Banach algebras and obtain characterizations of module character contractible Banach algebras in terms of the existence of module $(ϕ,φ)$-diagonals. We introduce module approximately character amenable Banach algebras. Finally, for every inverse semigroup $S$ with subsemigroup $E$ of idempotents, we find necessary and sufficient conditions for the $\ell^1(S)$ and its second dual to be module approximate character amenable (as a $…
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