Results 21 to 30 of about 722 (111)
On a functional equation that has the quadratic-multiplicative property
Open Mathematics, 2020 In this article, we obtain the general solution and prove the Hyers-Ulam stability of the following quadratic-multiplicative functional equation:ϕ(st−uv)+ϕ(sv+tu)=[ϕ(s)+ϕ(u)][ϕ(t)+ϕ(v)]\phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t)+\phi (v ...
Park Choonkil +4 more
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Sine Subtraction Laws on Semigroups
Annales Mathematicae Silesianae, 2023 We consider two variants of the sine subtraction law on a semi-group S. The main objective is to solve f(xy∗ ) = f(x)g(y) − g(x)f(y) for unknown functions f, g : S → ℂ, where x ↦ x* is an anti-homomorphic involution.
Ebanks Bruce
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The stability of an additive (ρ_1, ρ_2)-functional inequality in Banach spaces
Journal of Mathematical Inequalities, 2019 In this paper, we introduce and solve the following additive (ρ1,ρ2) -functional inequality ‖ f (x+ y)− f (x)− f (y)‖ ‖ρ1( f (x+ y)+ f (x− y)−2 f (x))‖ (1) + ∥∥∥ρ2 ( 2 f ( x+ y 2 ) − f (x)− f (y) ∥∥∥ , where ρ1 and ρ2 are fixed nonzero complex numbers ...
Choonkill Park
semanticscholar +1 more source
Approximately Vanishing of Topological Cohomology Groups [PDF]
, 2005 In this paper, we establish the Pexiderized stability of coboundaries and cocycles and use them to investigate the Hyers--Ulam stability of some functional equations. We prove that for each Banach algebra $A$, Banach $A$-bimodule $X$ and positive integer
Bade +20 more
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Approximation of quadratic Lie ∗-derivations on ρ-complete convex modular algebras
, 2020 In this paper, we investigate stable approximation of almost quadratic Lie ∗ -derivations associated with approximate quadratic mappings on ρ -complete convex modular algebras χρ by using Δ2 -condition via convex modular ρ.
Hark-Mahn Kim +2 more
semanticscholar +1 more source
On the stability of the orthogonal Pexiderized Cauchy equation [PDF]
, 2004 We investigate the stability of Pexiderized mappings in Banach modules over a unital Banach algebra. As a consequence, we establish the Hyers--Ulam stability of the orthogonal Cauchy functional equation of Pexider type $f_1(x+y)=f_2(x)+f_3(y)$, $x\perp y$
Aczél +19 more
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The Cosine-Sine Functional Equation on Semigroups
Annales Mathematicae Silesianae, 2022 The primary object of study is the “cosine-sine” functional equation f(xy) = f(x)g(y)+g(x)f(y)+h(x)h(y) for unknown functions f, g, h : S → ℂ, where S is a semigroup.
Ebanks Bruce
doaj +1 more source
A Variant of D’Alembert’s Functional Equation on Semigroups with Endomorphisms
Annales Mathematicae Silesianae, 2022 Let S be a semigroup, and let φ, ψ: S → S be two endomorphisms (which are not necessarily involutive). Our main goal in this paper is to solve the following generalized variant of d’Alembert’s functional equation f(xϕ(y))+f(ψ(y)x)=2f(x)f(y), x,y ∈ S,
Akkaoui Ahmed +2 more
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On the generalized Hyers-Ulam-Rassias stability problem of radical functional equations
Journal of Inequalities and Applications, 2012 In this paper, the generalized Hyers-Ulam-Rassias stability problem of radical quadratic and radical quartic functional equations in quasi-β-Banach spaces and then the stability by using subadditive and subquadratic functions for radical functional ...
S. Kim, Y. Cho, M. Eshaghi Gordji
semanticscholar +1 more source
Functional Equations and Fourier Analysis
, 2010 By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d ...
Akkouchi +5 more
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