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- W2891184023 abstract "Two years ago, during the 21st European Conference on Iteration Theory, Gregory Derfel asked: “Does there exist a non-trivial bounded continuous solution of the equation $$2f(x) = f(x-1) + f(-2x)$$ ?” He repeated the question during the 55th International Symposium on Functional Equations. In this paper we present a partial solution of a more general problem, connected to the functional equation $$f(x) = M big ( f(x+t_{1}), f(x + t_{2} ),ldots , f(x + t_{n-1} ), ,f(ax) big ),$$ where $$n in mathbb {N}, ,t_{1},t_{2},ldots ,t_{n-1} in mathbb {R} {setminus } { 0}, ,a in (-infty , 0)$$ and M is a given function in n variables satisfying some additional properties. In particular, M can be a weighted quasi-arithmetic mean in n variables." @default.
- W2891184023 created "2018-09-27" @default.
- W2891184023 creator A5010690638 @default.
- W2891184023 date "2018-09-05" @default.
- W2891184023 modified "2023-10-05" @default.
- W2891184023 title "On a functional equation related to a problem of G. Derfel" @default.
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- W2891184023 doi "https://doi.org/10.1007/s00010-018-0600-5" @default.
- W2891184023 hasPublicationYear "2018" @default.
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