On a generalization of the Shannon functional inequality. (English) Zbl 0674.94005
Summary: The well known Shannon entropy \(-\sum p_ k\log p_ k\) satisfies the inequality \(-\sum p_ k\log p_ k\leq -\sum p_ k\log q_ k.\) Extensive studies have been made on the inequality \(\sum p_ kf_ k(q_ k)\leq \sum p_ kf_ k(p_ k)\) which contains the above inequality as a special case. In this paper, we consider the most general inequality \(\sum g_ k(p_ k)f_ k(p_ k)\geq \sum g_ k(p_ k)f_ k(q_ k)\) of the above type and obtain its general solution on an open domain.
Keywords:
Shannon entropyReferences:
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