Let f z szqΓ a z be the sequence of partial sums of a function a z that is analytic in z -1 and either starlike of order β£ or ks 2 k Γ 4 convex of order β£, 0 F β£ -1. When the coefficients a are ''small,'' we deterk Γ Ε½ . Ε½ 4 Γ Ε½ . Ε½ .4 Γ Ε½ . X Ε½ .4 mine lower bounds on Re f z rf z , Re f z rf z , R
Ratio prophet inequalities for convex functions of partial sums
β Scribed by Michael J. Klass
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 228 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0167-7152
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π SIMILAR VOLUMES
is non-decreasing. Thus, if one applies the c,-inequality, the inequality follows trivially. From this and from the preceding inequality we obtain By our condition the sums on the right hand side converge to 0 as n -+ + 00. This proves the assertion. Remarks. It is easy to see that for p > 2 our c
Let P be a finite poset and let x, y e P. Let C be a finite chain. Define NS(i, j) to be the number of strict order-preserving maps to: P--~C satisfying to(x)=i and to(y)=j. Various inequalities are proved, commencing with Theorem 2: If r, s, t, u, v, w are non-negative integers then NS(r, u + v + w
In this paper we prove some known and new inequalities using an elementary inequality and some basic facts from differential calculus.