riesz s argument for minkowski s inequality
Báo cáo hóa học: " On Minkowski’s inequality and its application" doc
... exponents are equal, i.e., 1/p = (1 /s + 1/t)/2 On the other hand, by using Minkowski s inequality for s >1 and t >1, respectively, we obtain 1 /s 1 /s ≤ (f (x) + g(x) )s dx f s (x)dx 1 /s + gs (x)dx ... reversed form of inequality (2.6) Acknowledgements The authors wish to thank the referee for his many excellent suggestions for improving the original manuscript This Research is supported by National ... n-dimensional Euclidean space ℝn(n >2) Associated with a compact subset K of ℝn, which is star-shaped with respect to the origin, is its radial function r(K, ·): Sn - ® ℝ, defined for u Î Sn - 1, by ρ(K,...
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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
... 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, ” ... and g x is strictly Since g x ≥ for x ≥ 1, g x is strictly increasing, g x ≥ g 0, g x is strictly increasing, and hence g x ≥ g for increasing, g x ≥ g x ≥ Proof of Proposition 2.13 Using Corollary ... Rk xk Since Qi pi ··· pk−1 Rk 1, this inequality is a consequence of Jensen s inequality Thus, the proof is completed 4.3 10 Journal of Inequalities and Applications Proof of Propositions Proof...
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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 ... and J Peˇ ari´ , “Generalizations of the Jensen inequality, ” Osterreichische Akademie der c c c Wissenschaften Mathematisch-Naturwissenschaftliche Klasse Sitzungsberichte, vol 196, no 1–3, pp...
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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
... function f 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 ... can choose any θ1 satisfying ≤ θ1 ≤ μ1 For n > 2, let us suppose that 1.3 has been proved for up to n − 1, and consider the case of n Fix x1 , , xn We may assume that all xk are distinct ... 1.14 k Define the set S by S p1 , , pn | pk ≥ 0, ∀k 1.15 We wish to show h p ≥ on the set S subject to the constraint p1 · · · pn Suppose the minimum of h p is in the interior of S By the Lagrange...
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Báo cáo hóa học: "Research Article On the Precise Asymptotics of the Constant in Friedrich’s Inequality for Functions " potx
... will be established Hence, it is possible to construct the lower and the upper bounds for Kε Proofs of the main results and some auxiliary results In Sections 3.1 and 3.2 we discuss, present, and ... fact this was our original interest in the subject The paper is organized as follows In Section 2, we present and discuss our main results In Section 3, these results are proved via some auxiliary ... results, which are of independent interest In Section 4, we consider partial cases, where it is possible to give the asymptotic expansion for the constant with respect to ε The main results It...
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Jensen’s Inequality
... r ,n g Sn ; and 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, ... 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: " Extension of Hu Ke’s inequality and its applications Jing-Feng Tian" pptx
... 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 reversed versions In Section ... inequalities Acknowledgements The author would like to express his sincere thanks to the anonymous referees for their making great efforts to improve this paper This work was supported by the NNSF of ... (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
... − s2 = s1 λc,ϕ,ψ (x) + − s1 λc, s1 , s2 (x) = for each x Î I\{c} Therefore, we have 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 ... 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 - ), it follows from hypothesis that each s is in C+ (I), and then s Î Csm, ... by Jensen s inequality This also means M (f) ≤ M ψ (f) because ψ is monotone decreasing on I For the strict case, since g is a non-constant function on Ω, we obtain the desired results from...
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Báo cáo hóa học: " On improvements of the Rozanova’s inequality" potx
... 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 ... high-order partial derivatives, see [14,15] For an extensive survey on these inequalities, see [16] The first aim of the present paper is to establish the following Opial-type inequality involving higher-order ... following inequality holds a b α β |D1 D2 x (s, t)| D1 D2 p (s, t) ∂ |x (s, t)| f p (s, t) · g ∂t p (s, t) |D1 D2 x (s, t)| b dsdt β D1 D2 p (s, t) · g D1 D2 p (s, t) D1 D2 p (s, t) · g a α ≤f s Proof Let y (s, ...
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Báo cáo sinh học: " Research Article Improvement and Reversion of Slater’s Inequality and Related Results" pdf
... 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 ... So by setting m in 3.35 , we 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 ... special case of 3.29 for r s1 , s s1 s2 /2 if s1 < s2 and for r s2 , s s1 , t s1 s2 /2 if s2 < s1 s2 , t Journal of Inequalities and Applications 13 Let Mt x be stated as above, define dt as dt ϕt...
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Báo cáo hóa học: " Research Article On the Strengthened Jordan’s Inequality" pot
... 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 ... 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 ... can see that sin x/x is not always less than a polynomial of (π − 4x2 ) with positive coefficients for all < x ≤ π/2 Sharpening Jordan s inequality The following monotone form of L’Hopital s rule...
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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
... 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 ... differential equation 1.2 has been done to the best of the author knowledge Motivated by these cases, as a part of this paper, we study the estimates of periods of periodic solutions for the differential ... 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 of...
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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 ... of Inequalities and Applications In 2006, Yang gave an extension of as follows If p > 1, 1/p 1/q 1, r > 1, 1/r 1 /s 1, t ∈ 0, , − min{r, s} t min{r, s} ≥ λ > p q − min{r, s} t, such that ∞ > ∞...
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Báo cáo hóa học: " Research Article Diamond-α Jensen’s Inequality on Time Scales" pdf
... scales as introduced in Hilger s 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 ... h s ♦α s , 3.7 then using 3.6 and item of Lemma 2.2, we get b h s f g 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 ... f t h s g β s ♦α s b a h s ♦α s h s ♦α s , if β < or β > 1; 3.11 , if β ∈ 0, ln t on 0, ∞ One can also see that f is concave h s |g s ♦α s b a h s ♦α s ≥ b a h s ln g s ♦α s b a h s ♦α s 3.12...
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Báo cáo hóa học: " Research Article Some New Results Related to Favard’s Inequality" pot
... 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, ... 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 ≥ ... 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:...
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Báo cáo hóa học: " Research Article Hilbert’s Type Linear Operator and Some Extensions of Hilbert’s Inequality" docx
... 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 ... 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 the ... 0, for y ∈ (0,1) 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...
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Báo cáo hóa học: " Research Article Hilbert’s Type Linear Operator and Some Extensions of Hilbert’s Inequality" doc
... 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 ... 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 the ... 0, for y ∈ (0,1) 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...
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Báo cáo hóa học: " Research Article New Strengthened Carleman’s Inequality and Hardy’s Inequality" ppt
... + 1/2 c (2.2) holds Furthermore, 4c/3 − 1/2 is the best constant in inequality (2.1) or 4c/3 + 1/2 is the best constant in inequality (2.2) Proof (i) We construct a function as f (x) = x ln + ... [11] S Kaijser, L.-E Persson, and A Oberg, “On Carleman and Knopp s inequalities,” Journal of Approximation Theory, vol 117, no 1, pp 140–151, 2002 [12] M Johansson, L.-E Persson, and A Wedestig, ... 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
... + 1/2 c (2.2) holds Furthermore, 4c/3 − 1/2 is the best constant in inequality (2.1) or 4c/3 + 1/2 is the best constant in inequality (2.2) Proof (i) We construct a function as f (x) = x ln + ... [11] S Kaijser, L.-E Persson, and A Oberg, “On Carleman and Knopp s inequalities,” Journal of Approximation Theory, vol 117, no 1, pp 140–151, 2002 [12] M Johansson, L.-E Persson, and A Wedestig, ... 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
... (1.4) In this paper, we show a new sharp and generalized version of Popoviciu s inequality, which is a unified improvement of Acz´ l s inequality and Popoviciu s inequality In e Section 4, the ... would like to express hearty thanks to the anonymous referees for valuable comments on this paper References [1] J Acz´ l, “Some general methods in the theory of functional equations in one variable ... 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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