polya s coaching and carleman s inequality

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 ... Journal of Inequalities in Pure and Applied Mathematics, vol 2, no 2, article 21, pp 1–4, 2001 ¨ [11] S Kaijser, L.-E Persson, and A Oberg, “On Carleman and Knopp s inequalities,” Journal of Approximation...

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Báo cáo hóa học: " Research Article New Strengthened Carleman’s Inequality and Hardy’s Inequality" docx

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... 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 ... Journal of Inequalities in Pure and Applied Mathematics, vol 2, no 2, article 21, pp 1–4, 2001 ¨ [11] S Kaijser, L.-E Persson, and A Oberg, “On Carleman and Knopp s inequalities,” Journal of Approximation...

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Báo cáo hóa học: " On Minkowski’s inequality and its application" doc

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... 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

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... 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

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... 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

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... 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 Jensen’s Inequality for Convex-Concave Antisymmetric Functions and Applications" pptx

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... 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

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... 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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Báo cáo hóa học: " Research Article Hilbert’s Type Linear Operator and Some Extensions of Hilbert’s Inequality" docx

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... 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 ... Assume that the constant factor D(A,B) in (2.6) is not the best possible, then there exist a positive real number K Journal of Inequalities and Applications with K < D(A,B), such that (2.6) is...

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Báo cáo hóa học: " Research Article Hilbert’s Type Linear Operator and Some Extensions of Hilbert’s Inequality" doc

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... 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 ... Assume that the constant factor D(A,B) in (2.6) is not the best possible, then there exist a positive real number K Journal of Inequalities and Applications with K < D(A,B), such that (2.6) is...

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Báo cáo hóa học: " Research Article Improvement of Aczél’s Inequality and Popoviciu’s Inequality" pdf

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... 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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AN ELEMENTARY PROOF OF BLUNDON’S INEQUALITY GABRIEL DOSPINESCU, MIRCEA LASCU, COSMIN POHOATA, AND MARIAN TETIVA

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... 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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Jensen’s Inequality

Danh mục: Cao đẳng - Đại học

... this last expression is the value of the European derivative security Of course, the LHS cannot be strictly less than the RHS above, since stopping at time n is always allowed, and we conclude ... g S = IE 1 + r,n g Sn : 94 S2 (HH) = 16 S (H) = S2 (HT) = S =4 S2 (TH) = S1 (T) = S2 (TT) = Figure 7.3: A three period binomial model 7.3 Stopped Martingales Let fYk gn=0 be a stochastic ... American call Assume that r Consider the American derivative security with payoff g Sk in period k The value of this security is the same as the value of the simple European derivative security...

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Báo cáo hóa học: " On improvements of the Rozanova’s inequality" potx

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... Opial s inequality and its generalizations, extensions and discretizations play a fundamental role in establishing the existence and uniqueness of initial and boundary value problems for ordinary and ... p (s, t)g ≤w x (s, t) p (s, t) · v D1 D2 p (s, t)g a b 0 D1 D2 p (s, t)g x (s, t) D1 D2 p (s, t) D1 D2 x (s, t) D1 D2 p (s, t) dsdt , dsdt (1:7) Zhao and Cheung Journal of Inequalities and Applications ... D1 D2 x (s, t) )dsdt ≤ w b D1 D2 x (s, t) dsdt 0 Acknowledgements The authors express their deep gratitude to the referees for their many very valuable suggestions and comments The research of...

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Báo cáo hóa học: " Research Article The Best Lower Bound Depended on Two Fixed Variables for Jensen’s Inequality with Ordered Variables" pot

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... 5.1 Since this inequality is homogeneous in and ak , and also in Qi and Rk , without loss of and Qi Using the notations ak x2 and Rk p, where generality, assume that x ≥ and p > 0, the inequality ... Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993 S S Dragomir, J Peˇ ari´ , and L E Persson, “Properties of some functionals related to Jensen s c c inequality, ” ... Rk The proposition is proved ak 5.13 12 Journal of Inequalities and Applications References D S Mitrinovi´ , J E Peˇ ari´ , and A M Fink, Classical and New Inequalities in Analysis, vol 61 of...

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Báo cáo hóa học: " Research Article On the Strengthened Jordan’s Inequality" pot

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... previous research on Jordan s inequality, in this paper, we present two methods of sharpening Jordan s inequality The first method shows that one can obtain new strengthened Jordan s inequalities from ... the first author established an identity which states that the function sin x/x is a power series of (π − 4x2 ) with positive coefficients for all x = This enables us to obtain a much better inequality ... “New strengthened Jordan s inequality and its applications,” Applied Mathematics Letters, vol 16, no 4, pp 557–560, 2003 [3] A McD Mercer, U Abel, and D Caccia, “Problems and solutions: solutions...

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Báo cáo hóa học: " Research Article A Generalized Wirtinger’s Inequality with Applications to a Class of Ordinary Differential Equations" docx

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... Inequalities and Applications For the special case that n and p 1, various problems on the solutions of 1.1 , such as the existence of periodic solutions, bifurcations of periodic solutions, and stability ... Nussbaum, “Uniqueness and nonuniqueness for periodic solutions of x t Journal of Diﬀerential Equations, vol 34, no 1, pp 25–54, 1979 P Dormayer, “The stability of special symmetric solutions ... delay and p is also considered by a lot of researchers see 7–13 Most of the work contained in literature on 1.1 is the existence and multiplicity of periodic solutions However, except the questions...

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Báo cáo hóa học: " Research Article A Hilbert’s Inequality with a Best Constant Factor" doc

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... 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 Diamond-α Jensen’s Inequality on Time Scales" pdf

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... s ♦α s − a b h s ♦α s f b a a b b h s f g s ♦α s − a h s g s ♦α s b a h s ♦α s h s ♦α s f t a b hs f g s − f t ♦α s a ≥ at 3.8 b hs g s −t ♦α s a b at a b at b h s g s ♦α s − t h s ♦α s a h s ... Equations on Time Scales, Birkh¨ user, Boston, Mass, USA, 2001 a 16 M Bohner and A Peterson, Eds., Advances in Dynamic Equations on Time Scales, Birkh¨ user, Boston, a Mass, USA, 2003 17 J W Rogers ... thesis see also 8, In Section 3, we present our main results which are generalizations of Jensen s inequality on time scales Some examples and applications are given in Section Preliminaries...

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Báo cáo hóa học: " Research Article Some New Results Related to Favard’s Inequality" pot

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... Jensen sense for s ≥ Note that s f is continuous for s ≥ since lim s f s 0 Δ0 f and lim s f s 1 Δ1 f 2.10 This implies s f is continuous; therefore, it is log-convex Since s f is log-convex, ... Functions, Partial Orderings, and Statistical Applications, c c vol 187 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1992 S Karlin and W J Studden, Tchebycheﬀ Systems: ... function see 4, page Lemma 1.9 If φ is convex on an interval I ⊆ R, then φ s1 s3 − s2 φ s2 holds for every s1 < s2 < s3 , s1 , s2 , s3 ∈ I Now, we will give our main results s1 − s3 φ s3 s2 − s1 ≥...

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