Results 11 to 20 of about 4,400 (261)
On stability of additive mappings [PDF]
International Journal of Mathematics and Mathematical Sciences, 1991 In this paper we answer a question of Th. M. Rassias concerning an extension of validity of his result proved in [3].
Zbigniew Gajda
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Functional Inequalities Associated with Additive Mappings [PDF]
Abstract and Applied Analysis, 2008 The functional inequality ‖f(x)+2f(y)+2f(z)‖≤‖2f(x/2+y+z)‖+ϕ (x,y,z) (x,y,z∈G) is investigated, where G is a group divisible by 2,f:G→X and ϕ:G3→[0,∞) are mappings, and X is a Banach space.
Jaiok Roh, Ick-Soon Chang
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On a $$\rho $$-Orthogonally Additive Mappings [PDF]
Results in Mathematics, 2020 AbstractWe show that a real normed linear space endowed with the$$\rho $$ρ-orthogonality relation, in general need not be an orthogonality space in the sense of Rätz. However, we prove that$$\rho $$ρ-orthogonally additive mappings defined on some classical Banach spaces have to be additive.
Chmieliński, Jacek +2 more
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On subadditive functions and ψ-additive mappings
Open Mathematics, 2003 Abstract In [4], assuming among others subadditivity and submultiplicavity of a function ψ: [0, ∞)→[0, ∞), the authors proved a Hyers-Ulam type stability theorem for “ψ-additive” mappings of a normed space into a normed space. In this note we show that the assumed conditions of the function ψ imply that ψ=0 and, consequently, every “ψ ...
Matkowski Janusz
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On Identities with Additive Mappings in Rings [PDF]
Iranian Journal of Mathematical Sciences and Informatics, 2020 Summary: If \(F,D:R\rightarrow R\) are additive mappings which satisfy \(F(x^ny^n)=x^ nF(y^n)+y^nD(x^n)\) for all \(x,y\in R\). Then, \(F\) is a generalized left derivation with associated Jordan left derivation \(D\) on \(R\). Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given
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Publications of the Research Institute for Mathematical Sciences, 1988 The set of observables of a Quantum Mechanical System need only be closed under a "quadratic" product. It is shown that an additive structure of this set (whose existence is less natural) is uniquely determined by this multiplicative structure.
Friedman, Yaakov, Hakeda, Josuke
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When are multiplicative mappings additive? [PDF]
Proceedings of the American Mathematical Society, 1969 Summary: A theorem of \textit{C. E. Rickart} [Bull. Am. Math. Soc. 54, 758--764 (1948; Zbl 0032.24904), Theorem II] is generalized as follows: Theorem. Let \(R\) be a ring containing a family \(\{e_\alpha\mid \alpha\in A\}\) of idempotents which satisfies: (1) \(xR=0\) implies \(x=0\); (2) if \(e_\alpha Rx=0\) for each \(\alpha\in A\), then \(x=0\); (3)
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Additive Maps on Units of Rings
Canadian Mathematical Bulletin, 2018 AbstractLet R be a ring. A map f: R → R is additive if f(a + b) = f(a) + f(b) for all elements a and b of R. Here, a map f: R → R is called unit-additive if f(u + v) = f(u) + f(v) for all units u and v of R. Motivated by a recent result of Xu, Pei and Yi showing that, for any field F, every unit-additive map of (F) is additive for all n ≥ z, this paper
Kosan, Tamer +2 more
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THE NEARLY ADDITIVE MAPS [PDF]
Bulletin of the Korean Mathematical Society, 2009 This note is a verification on the relations between almost lin- ear and nearly additive maps; and the continuity of almost multiplicative nearly additive maps. Also we consider the stability of nearly additive and almost linear maps.
Esmaeeil Ansari-Piri, Nasrin Eghbali
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On the Stability of Cauchy Additive Mappings
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2008 The following inequality and the two other of similar type is considered: \[ \| f(x)+f(y)+f(z)\| \leq \left\| 2f\left(\frac{x+y+z}{2}\right)\right\| ,\qquad x,y,z\in X\tag{1} \] where \(f\colon X\to Y\), \(X,Y\) are Banach spaces. It is easy to see that a solution of the above inequality has to be an additive mapping.
Jun, Kil-Woung, Roh, Jaiok
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