Let $\mathcal {A} $ be a $ C^* $-algebra acting on a Hilbert space $\mathcal {H} $, let
$\sigma:\mathcal {A}\to B (\mathcal {H}) $ be a linear map** and let $ d:\mathcal {A}\to B …

In this paper, we introduce and solve the following additive s-functional inequality: 0.1 ‖
f\left (x+ y\right)-f (x)-f (y)\right ‖ ≤ ‖ s (f (xy)-f (x)-f (-y)) ‖, fx+ yf (x)-f (y)≤‖ s (f (xy)-f (x)-f …

Let 𝒜 be an algebra. A sequence {dn} of linear map**s on 𝒜 is called a higher derivation if
for each a, b∈ 𝒜 and each non-negative integer n. In this article, we show that if {dn} is a …

In this paper, we introduce and solve the following additive (ρ< sub> 1, ρ< sub> 2)-functional
inequalities‖ f (x+ y+ z)− f (x)− f (y)− f (z)‖≤‖ ρ 1 (f (x+ z)− f (x)− f (z))‖+‖ ρ 2 (f (y+ z)− f …

Various notions of amenability in Banach algebras - ScienceDirect Skip to main contentSkip
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Let A be a Banach algebra and σ, τ be continuous homomorphisms on A. Suppose that X be
a Banach A-bimodule. A linear map** d: A−→ X is a (σ, τ)-derivation if d (ab)= d (a) σ (b)+ …

In this paper, we introduce bihom derivations in complex Banach algebras. Using the fixed
point method and the direct method, we prove the Hyers–Ulam stability of bihom derivations …

‎ Let $\mathcal {A} $ and $\mathcal {B} $ be two Banach algebras and let‎‎ $\mathcal {M} $ be
a Banach $\mathcal {B} $-bimodule‎.‎ Suppose that‎‎ $\sigma:\mathcal {A}\rightarrow\mathcal …

In this paper, we solve an additive σ-random operator inequality and by the fixed point
technique we get an approximation of mentioned additive σ-random operator in fuzzy …

Let $ A $ be a Banach algebra and let $\varphi $ and $\psi $ be continuous homomorphisms
on $ A $. We consider the following module actions on $ A $, $$ a\cdot x=\varphi (a) …