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761.
762.
The k‐th power of a graph G, denoted by , is a graph with the same set of vertices as G such that two vertices are adjacent in if and only if their distance in G is at most k. In this paper, we give the bounds on the spectral radius of and . The Nordhaus–Gaddum‐type inequality for the spectral radius of the graph is also presented. Moreover, we obtain an upper bound on the energy of the second power of graphs. 相似文献
763.
In this paper we present new results on two‐weight Hardy, Hardy–Poincaré and Rellich type inequalities with remainder terms on a complete noncompact Riemannian Manifold M. The method we use is flexible enough to obtain more weighted Hardy type inequalities. Our results improve and include many previously known results as special cases. 相似文献
764.
On the norm of a Hilbert's type linear operator and applications 总被引:1,自引:0,他引:1
Bicheng Yang 《Journal of Mathematical Analysis and Applications》2007,325(1):529-541
In this paper, the norm of a Hilbert's type linear operator is given. As applications, a new operator inequality and the equivalent forms with the norm are obtained, and particularly some new extended Hilbert's type inequalities and the equivalent forms with the best constant factors are established. 相似文献
765.
Jorge Antezana Demetrio Stojanoff 《Journal of Mathematical Analysis and Applications》2007,331(1):297-307
Let A be a C∗-algebra and be a positive unital map. Then, for a convex function defined on some open interval and a self-adjoint element a∈A whose spectrum lies in I, we obtain a Jensen's-type inequality f(?(a))??(f(a)) where ? denotes an operator preorder (usual order, spectral preorder, majorization) and depends on the class of convex functions considered, i.e., monotone convex or arbitrary convex functions. Some extensions of Jensen's-type inequalities to the multi-variable case are considered. 相似文献
766.
Szymon W?sowicz 《Journal of Mathematical Analysis and Applications》2007,332(2):1229-1241
It is well known that every convex function (where I⊂R is an interval) admits an affine support at every interior point of I (i.e. for any x0∈IntI there exists an affine function such that a(x0)=f(x0) and a?f on I). Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree no greater than the order of convexity. In this paper the attaching method is developed. It is applied to obtain the general result—Theorem 2, from which the mentioned above support theorem and some related properties of convex functions of higher (both odd and even) order are derived. They are applied to obtain some known and new Hadamard-type inequalities between the quadrature operators and the integral approximated by them. It is also shown that the error bounds of quadrature rules follow by inequalities of this kind. 相似文献
767.
Kil-Woung Jun 《Journal of Mathematical Analysis and Applications》2007,332(2):1335-1350
In this paper, we solve the generalized Hyers-Ulam-Rassias stability problem for Euler-Lagrange type cubic functional equations
f(ax+y)+f(x+ay)=(a+1)2(a−1)[f(x)+f(y)]+a(a+1)f(x+y) 相似文献
768.
Omer Friedland 《Journal of Functional Analysis》2007,251(2):492-497
Let ‖⋅‖ be a norm on Rn. Averaging ‖(ε1x1,…,εnxn)‖ over all the n2 choices of , we obtain an expression |||x||| which is an unconditional norm on Rn. Bourgain, Lindenstrauss and Milman [J. Bourgain, J. Lindenstrauss, V.D. Milman, Minkowski sums and symmetrizations, in: Geometric Aspects of Functional Analysis (1986/1987), Lecture Notes in Math., vol. 1317, Springer, Berlin, 1988, pp. 44-66] showed that, for a certain (large) constant η>1, one may average over ηn (random) choices of and obtain a norm that is isomorphic to |||⋅|||. We show that this is the case for any η>1. 相似文献
769.
Karen Avetisyan Miroslav Pavlovi? 《Journal of Mathematical Analysis and Applications》2007,336(1):31-43
It is proved that the inequality δX(ε)?cεp, p?2, where δX is the modulus of convexity of X, is sufficient and necessary for the inequality
770.
For any , a truncated symmetric α-stable process is a symmetric Lévy process in with a Lévy density given by for some constant c. In this paper we study the potential theory of truncated symmetric stable processes in detail. We prove a Harnack inequality
for nonnegative harmonic functions of these processes. We also establish a boundary Harnack principle for nonnegative functions
which are harmonic with respect to these processes in bounded convex domains. We give an example of a non-convex domain for
which the boundary Harnack principle fails.
The research of Panki Kim is supported by Research Settlement Fund for the new faculty of Seoul National University. The research
of Renming Song is supported in part by a joint US-Croatia grant INT 0302167. 相似文献