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 International Journal of Mathematics and Mathematical Sciences , 1997, DOI: 10.1155/s0161171297000264 Abstract: An extension is given for the inverse to H lder's inequality obtained recently by Zhuang.
 Xiaojing Yang International Journal of Mathematics and Mathematical Sciences , 2000, DOI: 10.1155/s0161171200003537 Abstract: We generalize the well-known Hölder inequality and give a condition at which theequality holds.
 Kenneth J Falconer Mathematics , 2014, Abstract: We establish an inequality which involves a non-negative function defined on the vertices of a finite $m$-ary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree summed over automorphisms of the tree, to a product of sums of powers of the function over vertices at certain levels of the tree. Conjugate powers arise naturally in the inequality, indeed, H\"{o}lder's inequality is a key tool in the proof which uses induction on subgroups of the automorphism group of the tree.
 Journal of Inequalities and Applications , 2002, Abstract: We prove: Let be real numbers with . Then we have for all real numbers : with the best possible exponents and . The left-hand side of (0.1) with is a discrete version of an integral inequality due to E.A. Milne [1]. Moreover, we present a matrix analogue of (0.1).
 Jang Lee-Chae Journal of Inequalities and Applications , 2009, Abstract: The purpose of this paper is to find H lder type inequality for the fermionic -adic invariant -integral which was defined by Kim (2008).
 Wing-Sum Cheung International Journal of Mathematics and Mathematical Sciences , 2001, DOI: 10.1155/s0161171201005658 Abstract: Some generalized Hölder's inequalities for positive as well as negative exponents are obtained.
 Journal of Function Spaces and Applications , 2005, DOI: 10.1155/2005/376150 Abstract: We introduce a class of spaces of infinite matrices similar to the class of Lebesgue spaces Lp(T), 1≤p≤∞, and we prove matriceal versions of Hölder inequality.
 Journal of Inequalities and Applications , 2006, Abstract: We prove the following let , and be real numbers, and let be positive real numbers with . The inequalities hold for all real numbers if and only if and . Furthermore, we provide a matrix version. The first inequality (with and ) is a discrete counterpart of an integral inequality published by E. A. Milne in 1925.
 Computer Science , 2015, Abstract: In 1994, Talagrand showed a generalization of the celebrated KKL theorem. In this work, we prove that the converse of this generalization also holds. Namely, for any sequence of numbers $00$, it is possible to find a roughly balanced Boolean function $f$ such that $\textrm{Inf}_j[f] < a_j$ for every $1 \le j \le n$.
 Journal of Inequalities and Applications , 2006, Abstract: We prove the following let α , β , a > 0 , and b > 0 be real numbers, and let w j ( j = 1 , … , n ; n ≥ 2 ) be positive real numbers with w 1 + … + w n = 1 . The inequalities α ∑ j = 1 n w j / ( 1 p j a ) ≤ ∑ j = 1 n w j / ( 1 p j ) ∑ j = 1 n w j / ( 1 + p j ) ≤ β ∑ j = 1 n w j / ( 1 p j b ) hold for all real numbers p j ∈ [ 0 , 1 ) ( j = 1 , … , n ) if and only if α ≤ min ( 1 , a / 2 ) and β ≥ max ( 1 , ( 1 min 1 ≤ j ≤ n w j / 2 ) b ) . Furthermore, we provide a matrix version. The first inequality (with α = 1 and a = 2 ) is a discrete counterpart of an integral inequality published by E. A. Milne in 1925.
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