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- W2969488046 abstract "The main purpose of this work is to provide the general solutions of a class of linear functional equations. Let $$nge 2$$ be an arbitrarily fixed integer, let further X and Y be linear spaces over the field $${mathbb {K}}$$ and let $$alpha _{i}, beta _{i}in {mathbb {K}}$$, $$i=1, ldots , n$$ be arbitrarily fixed constants. We will describe all those functions $$f, f_{i, j}:Xtimes Yrightarrow {mathbb {K}}$$, $$i, j=1, ldots , n$$ that fulfill the functional equation $$begin{aligned}&fleft( sum _{i=1}^{n}alpha _{i}x_{i}, sum _{i=1}^{n}beta _{i}y_{i}right) = sum _{i, j=1}^{n}f_{i, j}(x_{i}, y_{j}) &quad left( x_{i}in X, y_{i}in Y, i=1, ldots , nright) . end{aligned}$$Additionally, necessary and sufficient conditions will also be given that guarantee the solutions to be non-trivial." @default.
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- W2969488046 date "2019-08-24" @default.
- W2969488046 modified "2023-10-06" @default.
- W2969488046 title "On a class of linear functional equations without range condition" @default.
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- W2969488046 doi "https://doi.org/10.1007/s00010-019-00672-7" @default.
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