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Part of 1969 Miklós Schweitzer

Problems(1)

Miklos Schweitzer 1969_3

Source:

10/15/2008
Let f(x) f(x) be a nonzero, bounded, real function on an Abelian group G G, g1,...,gk g_1,...,g_k are given elements of G G and λ1,...,λk \lambda_1,...,\lambda_k are real numbers. Prove that if ∑i=1kλif(gix)≥0 \sum_{i=1}^k \lambda_i f(g_ix) \geq 0 holds for all x∈G x \in G, then ∑i=1kλi≥0. \sum_{i=1}^k \lambda_i \geq 0. A. Mate
functionabstract algebragroup theoryreal analysisreal analysis unsolved