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1
Content available remote On the stability of orthogonal additivity
EN
We deal with the stability of the orthogonal additivity equation, presenting a new approach to the proof of a 1995 result of R, Ger and the second author. We sharpen the estimate obtained there. Moreover, we work in more general settings, providing an axiomatic framework which covers much more cases than considered before by other authors.
2
Content available remote On the equation of the p-orthogonal additivity
EN
We solve a conditional functional equation of the form x ⊥y ⇒ f(x + y) = f(x) + f(y), where f is a mapping from a real normed linear space (X, k ź k) with dimX ≥2 into an abelian group (G, +) and ⊥ is a given orthogonality relation associated to the norm.
EN
We study the stability of some functional equations postulated for orthogonal vectors in a ball centered at the origin. The maps considered are denned on a finite-dimensional normed linear space with Birkhoff-James orthogonality and take their values in a real sequentially complete linear topological space. The main results establish the stability of the corresponding conditional Cauchy functional equation on a half-ball and in uniformly convex spaces on a whole ball. The methods used in the first part of the paper are similar to those from [10]. Since, however, now in a general structure, some additional problems arise, we need several new tools.
4
Content available remote Orthogonal stability of the Cauchy equation on balls
EN
We deal with stability of some functional equations postulated for orthogonal vectors in a ball centered at the origin. The maps considered are defined on a finite dimensional inner product space and take their values in a real sequentially complete linear topological space. The main result establishes the stability of the corresponding conditional Cauchy functional equation and as a consequence we obtain some other stability resuits. Results which do not involve the orthogonality relation are considered in more general structures.
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