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1.
It is proved that ifX andY are linear spaces andF :X p(Y) is a set-valued map with convex graph such thatF(x) Ø for allx X andF(x
0) is a singleton for somex
0, thenF is single-valued and affine. Applications to metric projections and to adjoints of set-valued maps are given.Supported by NSF Grant DMS-9100228.The main result of this paper has been obtained while the second author was visiting the Pennsylvania State University in the framework of the exchange agreement between the Romanian Academy and the National Academy of Sciences of the U.S.A. 相似文献
2.
It is shown that the problem of the best uniform approximation in the Hausdorff metric of a continuous set-valued map with finite-dimensional compact convex images by constant set-valued maps whose images are balls in some norm can be reduced to a visual geometric problem. The latter consists in constructing a spherical layer of minimal thickness which contains the complement of a compact convex set to a larger compact convex set. 相似文献
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Dušan Repovš Pavel V. Semenov 《Journal of Mathematical Analysis and Applications》2006,314(2):537-545
We apply the selection theorem for multivalued mappings with paraconvex values (rather than various versions of KKM-principle) to prove several minimax theorems. In contrast with well-known minimax theorems for coordinatewise semicontinuous functions, in our theorems finite intersections of sublevel or uplevel sets can be nonempty and nonconnected. 相似文献
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D. B. Rokhlin 《Mathematical Notes》2007,81(3-4):543-548
For set-valued random sequences (G n) n=0 N with relatively open convex values G n(ω), we prove a new test for the existence of a sequence (x n) n=0 N of selectors adapted to the filtration and admitting an equivalent martingale measure. The statement is formulated in terms of the supports of regular upper conditional distributions of G n. This is a strengthening of the main result proved in our previous paper [1], where the openness of the set G n(ω) was assumed and a possible weakening of this condition was discussed. 相似文献
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Jack T. Markin 《Journal of Mathematical Analysis and Applications》2006,321(2):862-866
We prove a continuous selection theorem for quasi-lower semicontinuous mappings with values that are closed sub-admissible subsets of a hyperconvex metric space and apply this result to obtain fixed point theorems in these spaces. 相似文献
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A. Amini-Harandi A.P. Farajzadeh 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5151-5156
Suppose X is a compact admissible subset of a hyperconvex metric spaces M, and suppose F:XM is a quasi-lower semicontinuous set-valued map whose values are nonempty admissible. Suppose also G:XX is a continuous, onto quasi-convex set-valued map with compact, admissible values. Then there exists an x0X such that As applications, we give some coincidence and fixed point results for weakly inward set-valued maps. Our results, generalize some well-known results in literature. 相似文献
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Yuto Ogata Tamaki Tanaka Yutaka Saito Gue Myung Lee Jae Hyoung Lee 《Optimization》2018,67(7):1067-1075
AbstractThis paper contains a generalized Gordan-type alternative theorem for set-valued maps which characterizes set relations without any convexity assumptions using certain evaluation functions. As a direct consequence and as a good example, we discuss robustness (or stability) of linear programming problems for modelling error. Moreover, this theorem can be utilized for that of general vector optimization problems in special cases due to reformation of the evaluation functions. 相似文献
9.
H. Ben-El-Mechaiekh W. Kryszewski 《Transactions of the American Mathematical Society》1997,349(10):4159-4179
We present new theorems on the existence of equilibria (or zeros) of convex as well as nonconvex set-valued maps defined on compact neighborhood retracts of normed spaces. The maps are subject to tangency conditions expressed in terms of new concepts of normal and tangent cones to such sets. Among other things, we show that if is a compact neighborhood retract with nontrivial Euler characteristic in a Banach space , and is an upper hemicontinuous set-valued map with nonempty closed convex values satisfying the tangency condition
then there exists such that Here, denotes a new concept of retraction tangent cone to at suited for compact neighborhood retracts. When is locally convex at coincides with the usual tangent cone of convex analysis. Special attention is given to neighborhood retracts having ``lipschitzian behavior', called retracts below. This class of sets is very broad; it contains compact homeomorphically convex subsets of Banach spaces, epi-Lipschitz subsets of Banach spaces, as well as proximate retracts. Our results thus generalize classical theorems for convex domains, as well as recent results for nonconvex sets.
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A new fixed point theorem and its applications 总被引:4,自引:0,他引:4
Xian Wu 《Proceedings of the American Mathematical Society》1997,125(6):1779-1783
In this paper, we first give a new fixed theorem of lower semicontinuous multivalued mappings, and then, as its applications we obtain some new equilibrium theorems for abstract economies and qualitative games.
12.
B. Satco 《Czechoslovak Mathematical Journal》2006,56(3):1029-1047
This paper presents a Komlós theorem that extends to the case of the set-valued Henstock-Kurzweil-Pettis integral a result
obtained by Balder and Hess (in the integrably bounded case) and also a result of Hess and Ziat (in the Pettis integrability
setting). As applications, a solution to a best approximation problem is given, weak compactness results are deduced and,
finally, an existence theorem for an integral inclusion involving the Henstock-Kurzweil-Pettis set-valued integral is obtained. 相似文献
13.
One of the most important problems in topology is the minimization (in some sense) of obstructions to extending a partial
map
, i.e., of a subsetF ⊂ Z/A such thatf can be globally extended to its complement. It is shown that ifZ is a fixed metric space with dimZ ≤ n andp, q ≥−1 are fixed numbers, then obstructions to extending all partial maps
can be concentrated in preselected fairly thin subsets ofZ.
Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 803–812, December 1997
Translated by O. V. Sipacheva 相似文献
14.
利用序理论和广义单调迭代法讨论了一类较为广泛的非线性不连续集值算子方程的数值解法,在给出离散格式后,进一步得到了若干收敛性的结果。 相似文献
15.
Let C be a nonempty subset of a topological vector space E. We state and prove new various fixed point theorems of Fan–Browder type for set-valued maps F:C→2E such that C⊂F(C) (called expansive), without assuming that the sets C and F(C) are convex or compact or equal, and E is Hausdorff. Let K be a convex subset of E and let C be a nonempty subset of K. Our proofs use a technique based on the investigations of the images of maps and restated for maps f:C×K→R∪{−∞,+∞} of G.X.-Z. Yuan’s results concerning the existence of equilibrium points and minimax inequalities for maps f:K×K→R∪{−∞,+∞}. Examples are provided. 相似文献
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§1Introductionandpreliminaries In1929,Knaster,Kuratowski,andMazurkiewicz(simply,KKM)[1]deducedthe celebratedKKMtheorem.TheKKMtheory,firstcalledbySehiePark,isthestudyof applicationsofvariousequivalentformulationsoftheclassicalKKMprinciple[2].Atthe beginning,thetheorywasmainlystudiedonconvexsubsetsofHausdorfftopologicalvector spaces[3],butlater,ithasbeenextendedtoconvexspacesbyLassonde[4],andtospaces havingcertainfamiliesofcontractiblesubsets(simply,C-spacesorH-spaces)by Horvath[5].Mor… 相似文献
19.
Jan Andres Tom Fürst Karel Pastor 《Journal of Mathematical Analysis and Applications》2008,340(2):1132-1144
A full analogy of the celebrated Sharkovsky cycle coexistence theorem is established for lower semicontinuous (multivalued) maps on metrizable linear continua. This result is further extended to triangular maps. 相似文献
20.
H. Ben-El-Mechaiekh S. Chebbi M. Florenzano 《Proceedings of the American Mathematical Society》1998,126(8):2345-2349
We present a simple and direct proof for a Leray-Schauder type alternative for a large class of condensing or compact set-valued maps containing convex as well as nonconvex maps.