hilbert s inequality and compensating dificulties

... B max {x, y } and give some new generalizations of Hilbert s inequality As applications, we also consider some particular results Yongjin Li et al Main results and applications Lemma 2.1 Define ... when ε is sufficiently small, which contradicts the hypothesis Hence the constant factor D(A,B) in (2.6) is the best possible and T = D(A,B) This completes the proof ∞ Theorem 2.3 Suppose that ... where the constant factors π and are both the best possible Let H be a real separable Hilbert space, and T : H →H be a bounded self-adjoint semipositive definite operator, then (see [4]) T (x,T...

Ngày tải lên: 22/06/2014, 06:20

... B max {x, y } and give some new generalizations of Hilbert s inequality As applications, we also consider some particular results Yongjin Li et al Main results and applications Lemma 2.1 Define ... when ε is sufficiently small, which contradicts the hypothesis Hence the constant factor D(A,B) in (2.6) is the best possible and T = D(A,B) This completes the proof ∞ Theorem 2.3 Suppose that ... where the constant factors π and are both the best possible Let H be a real separable Hilbert space, and T : H →H be a bounded self-adjoint semipositive definite operator, then (see [4]) T (x,T...

Ngày tải lên: 22/06/2014, 06:20

... f(x) + g(x) is constant or 1/p = (1 /s + 1/t)/2 On the other hand, in view of Minkowski s inequality for the cases of < s

Ngày tải lên: 20/06/2014, 22:20

... purpose of this work is to give extensions of inequalities (3) and (4) and establish their corresponding reversed versions Moreover, the obtained results will be applied to improve Hao Z-C inequality ... inequality [31] and Beckenbach-type inequality that is due to Wang [32] The rest of this paper is organized as follows In Section 2, we present extensions of (3) and (4) and establish their corresponding ... (27) The classical arithmetic-geometric mean inequality is one of the most important inequalities in analysis This classical inequality has been widely studied by many authors, and it has motivated...

Ngày tải lên: 20/06/2014, 22:20

... λc, s1 , s2 (x) = s2 λc,ϕ,ψ (x) + − s2 (s1 = 0) (3) and λc, s1 , s2 (x) = s2 s − s1 − s1 s1 λc,ϕ,ψ (x) − s1 −1 s1 (s1 = 0) (4) for each x Î I\{c} If s1 = 0, then it is trivial by (3) that λc, s1 ... first result asserts that a -mean function: ∇ ® M (f) is well defined and order preserving, and this assertion simultaneously gives a new interpretation of Jensen s inequality However, this ... function: s ® M(1 -s)  +s (f) is strictly monotone increasing and continuous on [0, ∞) Proof (i) Suppose that ϕ, ψ − ϕ ∈ C+ (I) For each s ≥ 1, put s = (1 - s)  + s Since sm s =  + s( ψ - ),...

Ngày tải lên: 21/06/2014, 00:20

... have special case of s1 s2 /2 if s1 < s2 and for t s1 , r s2 , and s s1 s2 /2 3.28 for t s1 , s s2 , and r if s2 < s1 Similarly by setting m in 3.36 , we have special case of 3.29 for r s1 , s s1 ... special case of s1 s2 /2 if s1 < s2 and for t s1 , r s2 , and s s1 s2 /2 if 3.39 for t s1 , s s2 , r s2 < s1 Similarly by setting m in 3.44 , we have special case of 3.40 for r s1 , s s2 , s1 ... s2 /2 if s2 < s1 and t s1 s2 /2 if s1 < s2 and for r s2 , s s1 , and t Acknowledgments The research of the first and second authors was funded by Higher Education Commission, Pakistan The research...

Ngày tải lên: 21/06/2014, 17:20

... constant factors, K and K p of 3.1 and 3.2 , are the best possible Proof We only prove that K is the best possible If the constant factor K in 3.1 is not the best possible, then there exists a ... this paper is to build a new Hilbert s inequality with a best constant factor and some parameters In the following, we always suppose that 1/p 1/q 1, p > 1, a ≥ 0, −1 < α < 1, both functions u ... This contracts the fact that H < K References G H Hardy, J E Littlewood, and G Polya, Inequalities, Cambridge University Press, Cambridge, UK, ´ 1952 B C Yang, “On Hilbert s inequality with some...

Ngày tải lên: 22/06/2014, 02:20

... 2002 [12] M Johansson, L.-E Persson, and A Wedestig, “Carleman s inequality- history, proofs and some new generalizations,” Journal of Inequalities in Pure and Applied Mathematics, vol 4, no 3, ... Mathematical Analysis and Applications, vol 234, no 2, pp 717–722, 1999 [3] P Yan and G.-Z Sun, “A strengthened Carleman s inequality, ” Journal of Mathematical Analysis and Applications, vol 240, no ... Mathematical Analysis and Applications, vol 253, no 2, pp 691–694, 2001 [8] X.-J Yang, “Approximations for constant e and their applications,” Journal of Mathematical Analysis and Applications, vol 262,...

Ngày tải lên: 22/06/2014, 06:20

... 2002 [12] M Johansson, L.-E Persson, and A Wedestig, “Carleman s inequality- history, proofs and some new generalizations,” Journal of Inequalities in Pure and Applied Mathematics, vol 4, no 3, ... Mathematical Analysis and Applications, vol 234, no 2, pp 717–722, 1999 [3] P Yan and G.-Z Sun, “A strengthened Carleman s inequality, ” Journal of Mathematical Analysis and Applications, vol 240, no ... Mathematical Analysis and Applications, vol 253, no 2, pp 691–694, 2001 [8] X.-J Yang, “Approximations for constant e and their applications,” Journal of Mathematical Analysis and Applications, vol 262,...

Ngày tải lên: 22/06/2014, 06:20

... version of Popoviciu s inequality, which is a unified improvement of Acz´ l s inequality and Popoviciu s inequality In e Section 4, the obtained result will be used to establish an integral inequality ... [14], Wu established a sharp and generalized version of Popoviciu s inequality as follows Theorem 1.3 Let p > 0, q > 0, 1/ p + 1/q ≥ 1, and let , bi (i = 1,2, ,n) be positive p p q q numbers such ... matical Analysis and Applications, vol 245, no 2, pp 393–403, 2000 [4] L Losonczi and Z P´ les, “Inequalities for indefinite forms,” Journal of Mathematical Analysis a and Applications, vol 205,...

Ngày tải lên: 22/06/2014, 18:20

... access and control profile It indicates the gender based access to resources, control over the use of resources and the benefits of the use of resources Access simply refers to the use of resources ... 2004) These socially induced differences between males and females result in discriminatory rewards, statuses, opportunities and roles as shall be discussed below Low educational level is one of ... employed to ascertain the statistical significance of differences and associations Specifically, t tests for difference of proportions and gross and net logistic regression models were applied...

Ngày tải lên: 05/03/2014, 13:20

Ngày tải lên: 16/03/2014, 03:20

... the states in E for consecutive members of the same dynasty In Section 4.1.2 we discuss these issues in detail 3.1.3 Preferences We assume that households value their consumption and leisure, and ... earnings process is consistent both with the U .S aggregate earnings and with the U .S earnings distribution; and in which the tax system resembles the U .S tax system In this article we provide such ... contributions to a social security system requires the inclusion of a second asset-type state variable in the household decision problem, and this increases the computational costs significantly This is...

Ngày tải lên: 29/03/2014, 20:20

... American country has experienced such deep distributional changes as Argentina (Gasparini and Sosa Escudero, 2001) This dissertation addresses the consequences of this inequality in distribution on ... relationship between distribution and growth, this dissertation attempts to test some hypotheses Since the research question is broken into several parts, the hypotheses follow a four-step scheme ... argues that a middle-class consensus promotes growth by encouraging stability, mass education, better public services, and property rights This “consensus” appears closely related to the social...

Ngày tải lên: 03/06/2014, 02:02

... Analysis and Applications, vol 235, no 2, pp 608–614, 1999 [8] J Kuang and L Debnath, “On new generalizations of Hilbert s inequality and their applications,” Journal of Mathematical Analysis and ... functions φ(x) and ψ(x) The other is to build a class of new inequalities similar to Hardy -Hilbert inequality (1.2) by introducing some parameters a, b, and c Some lemmas First, we give the β function ... Gao, “On Hilbert s inequality and its applications,” Journal of Mathematical Analysis and Applications, vol 212, no 1, pp 316–323, 1997 [3] B Yang, “Some generalizations of the Hardy -Hilbert integral...

Ngày tải lên: 21/06/2014, 22:20

... Inequalities and Applications holds for every x, y ∈ I It is clear that every convex function is Jensen-convex To see that the class of convex functions is a proper subclass of Jensen-convex functions, ... proof, see 2, page 71 or 1, page 53 A class of functions which is between the class of convex functions and the class of Jensen-convex functions is the class of Wright-convex functions A function ... Orderings, and Statistical Applications, c c vol 187 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1992 G Hardy, J E Littlewood, and G Polya, Inequalities, Cambridge...

Ngày tải lên: 22/06/2014, 02:20

... for various unknown weight vectors p This is why the statement of Theorem 1.2 makes the assumption that this is true for all possible weight vectors The following lemma gives a simple sufficient ... Equation 1.11 is true if and only if θ1 ≤ 1−f t x1 /f x − θ1 σ − q tx1 1.12 The right-hand side The cases q or t not pose problems because the right-hand side is still finite is an increasing function ... Theorem 1.2 Suppose that f x is strictly increasing, strictly concave, and twice continuously differentiable on a nonempty interval I ⊆ R, and suppose that f x is strictly convex on I Suppose that...

Ngày tải lên: 22/06/2014, 03:20

... two of the numbers to be less than or equal to (neither can all the numbers be less than 1) Because if a number is less than and two are greater than the inequality is obviously true (the product ... occurs if and only if ABC is equilateral Proof According to the well-known formulae cot A = s( s − a) , (s − b) (s − c) cot B = we deduce that cot s( s − b) , (s − c) (s − a) A = cot cot C = s( s − ... ≤ − 10 Proof Since the numbers are positive, from the given condition it follows immediately that x < xyz ⇔ yz > 1, and similarly xz > and yz > 1, which shows that it is not possible for two...

Ngày tải lên: 15/08/2014, 17:07

... mamma was sitting She was evidently oppressed by her isolation, and she was longing to express herself, to share her impressions with some one, to open her heart "He 's gone," she muttered, seeing ... a minute, sir, in a minute," says Pelageya She rushes out of the hut, and soon afterwards comes back with a bit of candle Yefim 's cheeks are rosy and his eyes are shining, and there is a peculiar ... Stepanov, is tossing from side to side on the floor She does not see him, but she hears him moaning and rolling on the floor from pain "His guts have burst," as he says; the pain is so violent...

Ngày tải lên: 06/11/2012, 14:13

Ngày tải lên: 25/01/2013, 16:44