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A generalized notion of n -weak amenability

Abasalt BodaghiBehrouz Shojaee — 2014

Mathematica Bohemica

In the current work, a new notion of n -weak amenability of Banach algebras using homomorphisms, namely ( ϕ , ψ ) - n -weak amenability is introduced. Among many other things, some relations between ( ϕ , ψ ) - n -weak amenability of a Banach algebra 𝒜 and M m ( 𝒜 ) , the Banach algebra of m × m matrices with entries from 𝒜 , are studied. Also, the relation of this new concept of amenability of a Banach algebra and its unitization is investigated. As an example, it is shown that the group algebra L 1 ( G ) is ( ϕ , ψ )- n -weakly amenable for any...

Mixed Type Of Additive And Quintic Functional Equations

Abasalt BodaghiPasupathi NarasimmanKrishnan RaviBehrouz Shojaee — 2015

Annales Mathematicae Silesianae

In this paper, we investigate the general solution and Hyers–Ulam–Rassias stability of a new mixed type of additive and quintic functional equation of the form [...] f(3x+y)−5f(2x+y)+f(2x−y)+10f(x+y)−5f(x−y)=10f(y)+4f(2x)−8f(x) f 3 x + y - 5 f 2 x + y + f 2 x - y + 10 f x + y - 5 f x - y = 10 f y + 4 f 2 x - 8 f x in the set of real numbers.

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