A Sharp Double Inequality between Seiffert, Arithmetic, and Geometric Means
Copyright policy ) Gong, Wei-Ming; Song, Ying-Qing; Wang, Miao-Kun; Chu, Yu-Ming;
A Sharp Double Inequality between Seiffert, Arithmetic, and Geometric Means
For fixed s ≥ 1 and any t1, t2 ∈ (0,1/2) we prove that the double inequality Gs(t1a + (1 − t1)b, t1b + (1 − t1)a)A1−s(a, b) < P(a, b) < Gs(t2a + (1 − t2)b, t2b + (1 − t2)a)A1−s(a, b) holds for all a, b > 0 with a ≠ b if and only if and . Here, P(a, b), A(a, b) and G(a, b) denote the Seiffert, arithmetic, and geometric means of two positive numbers a and b, respectively.
- Huzhou University China (People's Republic of)
- Hunan City University China (People's Republic of)
geometric mean, Seiffert mean, QA1-939, Inequalities for sums, series and integrals, Mathematics, arithmetic mean
geometric mean, Seiffert mean, QA1-939, Inequalities for sums, series and integrals, Mathematics, arithmetic mean
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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