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1.
J. C. Rosales 《Proceedings of the American Mathematical Society》2006,134(12):3417-3421
In this paper we study and characterize those Diophantine inequalities whose set of solutions is a symmetric numerical semigroup.
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Agnieszka Ka?amajska Katarzyna Pietruska-Pa?uba 《Central European Journal of Mathematics》2012,10(6):2033-2050
We obtain Hardy type inequalities $$\int_0^\infty {M\left( {\omega \left( r \right)\left| {u\left( r \right)} \right|} \right)\rho \left( r \right)dr} \leqslant C_1 \int_0^\infty {M\left( {\left| {u\left( r \right)} \right|} \right)\rho \left( r \right)dr + C_2 \int_0^\infty {M\left( {\left| {u'\left( r \right)} \right|} \right)\rho \left( r \right)dr,} }$$ and their Orlicz-norm counterparts $$\left\| {\omega u} \right\|_{L^M (\mathbb{R}_ + ,\rho )} \leqslant \tilde C_1 \left\| u \right\|_{L^M (\mathbb{R}_ + ,\rho )} + \tilde C_2 \left\| {u'} \right\|_{L^M (\mathbb{R}_ + ,\rho )} ,$$ with an N-function M, power, power-logarithmic and power-exponential weights ??, ??, holding on suitable dilation invariant supersets of C 0 ?? (?+). Maximal sets of admissible functions u are described. This paper is based on authors?? earlier abstract results and applies them to particular classes of weights. 相似文献
3.
Summary We investigate generalizations of the classical Jensen and Chebyshev inequalities. On one hand, we restrict the class of functions and on the other we enlarge the class of measures which are allowed. As an example, consider the inequality (J)(f(x) d) A (f(x) d, d d = 1. Iff is an arbitrary nonnegativeL
x
function, this holds if 0, is convex andA = 1. Iff is monotone the measure need not be positive for (J) to hold for all convex withA = 1. If has higher monotonicity, e.g., is also convex, then we get a version of (J) withA < 1 and measures that need not be positive. 相似文献
4.
P. Cubiotti 《Journal of Optimization Theory and Applications》1992,72(3):577-582
In this paper, given a nonempty closed convex setX ? n , a functionf: X→? n , and a multifunction Γ:X→2X, we deal with the problem of finding a point \(\hat x\) ∈X such that $$\hat x \in \Gamma (\hat x) and \langle f(\hat x), \hat x - y\rangle \leqslant 0, for all y \in \Gamma (\hat x).$$ For such problem, we establish a result where, in particular, the functionf is not assumed to be continuous. More precisely, we extend to the present setting a finite-dimensional version of a result by Ricceri on variational inequalities (Ref. 1). 相似文献
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J.L. Brenner 《Journal of Mathematical Analysis and Applications》1985,106(2):427-442
Sharp inequalities are derived for certain (polynomial-like) functions of the real variables pi (i = 1(1)σ) by interpreting pi as the probabilities that various switches be thrown in certain directions. Parameters mv in the inequalities are at first taken to be integers; later the inequalities are established when mv are arbitrary real numbers. The side condition ∑pi = 1 occurs throughout analysis, so there are many corollaries. Examples of the inequalities established are valid ifm>1 valid if m > 1, n > r + 1, 0 < p, s, p + s ? 1, and also valid if . (1.03) 相似文献
6.
Bounds for several integrals (tail probabilities, for example) are established by showing that each integral is a Schur function. 相似文献
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In this paper, we shall investigate the symmetry property of a multivariate orthogonal M-refinable function with a general dilation matrix M. For an orthogonal M-refinable function such that is symmetric about a point (centro-symmetric) and provides the approximation order k, we show that must be an orthogonal M-refinable function that generates a generalized coiflet of order k. Next, we show that there does not exist a real-valued compactly supported orthogonal 2Is-refinable function in any dimension such that is symmetric about a point and generates a classical coiflet. Finally, we prove that if a real-valued compactly supported orthogonal dyadic refinable function L2(Rs) has the axis symmetry, then cannot be a continuous function and can provide the approximation order at most one. The results in this paper may provide a better picture about symmetric multivariate orthogonal refinable functions. In particular, one of the results in this paper settles a conjecture in [D. Stanhill, Y.Y. Zeevi, IEEE Trans. Signal Process. 46 (1998), 183–190] about symmetric orthogonal dyadic refinable functions. 相似文献
8.
Mercedes H. Rosas Bruce E. Sagan 《Transactions of the American Mathematical Society》2006,358(1):215-232
Consider the algebra of formal power series in countably many noncommuting variables over the rationals. The subalgebra of symmetric functions in noncommuting variables consists of all elements invariant under permutation of the variables and of bounded degree. We develop a theory of such functions analogous to the ordinary theory of symmetric functions. In particular, we define analogs of the monomial, power sum, elementary, complete homogeneous, and Schur symmetric functions as well as investigating their properties.
9.
《Indagationes Mathematicae》2022,33(1):255-278
The characters of the (total) Springer representations afford the Green functions, that can understood as generalizations of Hall–Littlewood’s -functions. In this paper, we present a purely algebraic proof that the (total) Springer representations of are -orthogonal to each other, and show that it is compatible with the natural categorification of the ring of symmetric functions. 相似文献
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B.A. Bhayo 《Journal of Mathematical Analysis and Applications》2011,380(2):768-781
We study vector functions of Rn into itself, which are of the form x?g(|x|)x, where g:(0,∞)→(0,∞) is a continuous function and call these radial functions. In the case when g(t)=tc for some c∈R, we find upper bounds for the distance of image points under such a radial function. Some of our results refine recent results of L. Maligranda and S.S. Dragomir. In particular, we study quasiconformal mappings of this simple type and obtain norm inequalities for such mappings. 相似文献
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Chin-Yuan Hu 《Journal of Mathematical Analysis and Applications》2005,309(1):336-352
In a recent paper, Matysiak and Szablowski [V. Matysiak, P.J. Szablowski, Theory Probab. Appl. 45 (2001) 711-713] posed an interesting conjecture about a lower bound of real-valued characteristic functions. Under a suitable moment condition on distributions, we prove the conjecture to be true. The unified approach proposed here enables us to obtain new inequalities for characteristic functions. We also show by example that the improvement in the bounds is significant if more information about the distribution is available. 相似文献
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M. I. Tsatsulin 《Mathematical Notes》1991,50(2):872-875
Translated from Matematicheski Zametki, Vol. 50, No. 2, pp. 146–151, August, 1991. 相似文献
18.
Árpád Baricz 《Journal of Mathematical Analysis and Applications》2006,319(2):450-459
Let up(x) be the generalized and normalized Bessel function depending on parameters b,c,p and let σ(r)=up(1−r2)/up(r2), r∈(0,1). Motivated by an open problem of Anderson, Vamanamurthy, and Vuorinen we prove that for all r1,r2∈(0,1) for certain conditions on the parameters b,c,p. 相似文献
19.
Nonconvex functions and variational inequalities 总被引:8,自引:0,他引:8
M. A. Noor 《Journal of Optimization Theory and Applications》1995,87(3):615-630
In this paper, we study some properties of a class of nonconvex functions, called semipreinvex functions, which includes the classes of preinvex functions and arc-connected convex functions. It is shown that the minimum of an arcwise directionally differentiable semi-invex functions on a semi-invex set can be characterized by a class of variational inequalities, known as variational-like inequalities. We use the auxiliary principle technique to prove the existence of a solution of a variational-like inequality and suggest a novel iterative algorithm. 相似文献
20.
黄龙光 《纯粹数学与应用数学》2001,17(4):314-317
研究拓扑向量空间半准内凸函数的特性,给出半内凸弧方向可微函数的最小值可由一类似变分不等式问题的解表示及一类广义变分不等式解的唯一性。 相似文献