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本文研究了Block定理覆盖圆问题.利用微分与积分估值法,对覆盖圆的半径做了更精确地估计,得到了两个相关定理,扩大了覆盖圆的范围. 相似文献
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Memudu O. Olatinwo 《Central European Journal of Mathematics》2008,6(4):610-621
In this paper, the concept of multi-valued weak contraction of Berinde and Berinde [8] for the Picard iteration in a complete
metric space is extended to the case of multi-valued weak contraction for the Jungck iteration in a complete b-metric space. While our main results generalize the recent results of Berinde and Berinde [8], they also extend, improve
and unify several classical results pertainning to single and multi-valued contractive mappings in the fixed point theory.
Our results also improve the recent results of Daffer and Kaneko [16].
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A method for solving Hilbert's boundary value problem with discontinuous coefficients is studied for a function single-valued
and analytic in an annulus in the case in which the solution may have power-law singularities at finitely many points on the
boundary of the annulus. To illustrate the results obtained, we consider an explosion problem for two pinching charges in
a homogenous medium with a circular cylinder lying in the flow caused by the explosion.
Translated fromMatematicheskie Zametki, Vol. 66, No. 1, pp. 135–144, July, 1999. 相似文献
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B. D. Gel’man 《Mathematical Notes》2005,78(1-2):194-203
In the present paper, we prove a fixed-point theorem for completely continuous multivalued mappings defined on a bounded convex closed subset X of the Hilbert space H which satisfies the tangential condition
, where T
X
(x) is the cone tangent to the set X at a point x. The proof of this theorem is based on the method of single-valued approximations to multivalued mappings. In this paper, we consider a simple approach for constructing single-valued approximations to multivalued mappings. This approach allows us not only to simplify the proofs of already-known theorems, but also to obtain new statements needed to prove the main theorem in this paper.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 212–222.Original Russian Text Copyright © 2005 by B. D. Gel’man. 相似文献
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R. A. Poliquin R. T. Rockafellar L. Thibault 《Transactions of the American Mathematical Society》2000,352(11):5231-5249
Recently Clarke, Stern and Wolenski characterized, in a Hilbert space, the closed subsets for which the distance function is continuously differentiable everywhere on an open ``tube' of uniform thickness around . Here a corresponding local theory is developed for the property of being continuously differentiable outside of on some neighborhood of a point . This is shown to be equivalent to the prox-regularity of at , which is a condition on normal vectors that is commonly fulfilled in variational analysis and has the advantage of being verifiable by calculation. Additional characterizations are provided in terms of being locally of class or such that is convex around for some 0$">. Prox-regularity of at corresponds further to the normal cone mapping having a hypomonotone truncation around , and leads to a formula for by way of . The local theory also yields new insights on the global level of the Clarke-Stern-Wolenski results, and on a property of sets introduced by Shapiro, as well as on the concept of sets with positive reach considered by Federer in the finite dimensional setting.
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It is shown that the sum and the product of two commuting Banach space operators with Dunford's property (C) have the single-valued extension property. 相似文献