hilbert s inequality and compensating dificulties
Báo cáo hóa học: " Research Article Hilbert’s Type Linear Operator and Some Extensions of Hilbert’s Inequality" docx
... 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...
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Báo cáo hóa học: " Research Article Hilbert’s Type Linear Operator and Some Extensions of Hilbert’s Inequality" doc
... 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...
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Báo cáo hóa học: " On Minkowski’s inequality and its application" doc
... 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
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Báo cáo hóa học: " Extension of Hu Ke’s inequality and its applications Jing-Feng Tian" pptx
... 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...
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Báo cáo hóa học: " A new interpretation of Jensen’s inequality and geometric properties of -means" pptx
... 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 - ),...
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Báo cáo sinh học: " Research Article Improvement and Reversion of Slater’s Inequality and Related Results" pdf
... 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...
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Báo cáo hóa học: " Research Article A Hilbert’s Inequality with a Best Constant Factor" doc
... 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...
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Báo cáo hóa học: " Research Article New Strengthened Carleman’s Inequality and Hardy’s Inequality" ppt
... 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,...
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Báo cáo hóa học: " Research Article New Strengthened Carleman’s Inequality and Hardy’s Inequality" docx
... 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,...
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Báo cáo hóa học: " Research Article Improvement of Aczél’s Inequality and Popoviciu’s Inequality" pdf
... 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,...
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Gender Inequality and Women’s Empowerment pdf
... 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...
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Accounting for the U.S. Earnings and Wealth Inequality by Ana Casta˜neda, Javier D´ıaz-Gim´enez and Jos´e-V´ıctor R´ıos-Rull∗ potx
... 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...
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inequality and economic growth evidence from argentina's provinces using spatial econometrics
... 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...
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Báo cáo hóa học: " Research Article New Inequalities Similar to Hardy-Hilbert Inequality and their Applications" pdf
... 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...
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Báo cáo hóa học: " Research Article Jensen’s Inequality for Convex-Concave Antisymmetric Functions and Applications" pptx
... 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...
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Báo cáo hóa học: " Research Article A Refinement of Jensen’s Inequality for a Class of Increasing and Concave Functions" pptx
... 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...
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AN ELEMENTARY PROOF OF BLUNDON’S INEQUALITY GABRIEL DOSPINESCU, MIRCEA LASCU, COSMIN POHOATA, AND MARIAN TETIVA
... 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...
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ThThe Cook's Wedding and Other Stories
... 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...
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