scholarly journals Existence and Generic Stability of Strong Noncooperative Equilibria of Vector-Valued Games

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3158
Author(s):  
Yu Zhang ◽  
Shih-Sen Chang ◽  
Tao Chen
Keyword(s):  
Equilibrium Point ◽  
Existence Theorem ◽  
Strong Equilibrium ◽  
Upper Semicontinuous ◽  
Generic Stability ◽  
Noncooperative Equilibrium ◽  
Point Set ◽  
Vector Valued ◽  
Point Vector

In this paper, we obtain an existence theorem of general strong noncooperative equilibrium point of vector-valued games, in which every player maximizes all goals. We also obtain an existence theorem of strong equilibrium point of vector-valued games with single-leader–multi-follower framework by using the upper semicontinuous of parametric strong noncooperative equilibrium point set of the followers. Moreover, we obtain some results on the generic stability of general strong noncooperative equilibrium point vector-valued games.

scholarly journals Existence Theorems ofε-Cone Saddle Points for Vector-Valued Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Tao Chen
Keyword(s):  
Saddle Point ◽  
Existence Theorem ◽  
Equilibrium Problem ◽  
Existence Result ◽  
Existence Theorems ◽  
Saddle Points ◽  
Vector Equilibrium Problem ◽  
Saddle Point Theorem ◽  
Vector Equilibrium ◽  
Vector Valued

A new existence result ofε-vector equilibrium problem is first obtained. Then, by using the existence theorem ofε-vector equilibrium problem, a weaklyε-cone saddle point theorem is also obtained for vector-valued mappings.

scholarly journals A general vector-valued variational inequality and its fuzzy extension

1998 ◽  
Vol 21 (4) ◽  
pp. 637-642 ◽  
Author(s):  
Sehie Park ◽  
Byung-Soo Lee ◽  
Gue Myung Lee
Keyword(s):  
Variational Inequality ◽  
Existence Theorem ◽  
Kkm Theorem ◽  
Vector Valued ◽  
General Vector

A general vector-valued variational inequality (GVVI) is considered. We establish the existence theorem for (GVVI) in the noncompact setting, which is a noncompact generalization of the existence theorem for (GVVI) obtained by Lee et al., by using the generalized form of KKM theorem due to Park. Moreover, we obtain the fuzzy extension of our existence theorem.

scholarly journals Upper semicontinuity of the lamination hull

2018 ◽  
Vol 24 (4) ◽  
pp. 1503-1510
Author(s):  
Terence L.J. Harris
Keyword(s):  
Convex Hull ◽  
Upper Semicontinuity ◽  
Symmetric Matrices ◽  
Compact Set ◽  
Upper Semicontinuous ◽  
Rank One ◽  
Point Set

Let  K ⊆ ℝ2×2 be a compact set, let Krc be its rank-one convex hull, and let L (K) be its lamination convex hull. It is shown that the mapping K ↦ L̅(K̅) is not upper semicontinuous on the diagonal matrices in ℝ2×2, which was a problem left by Kolář. This is followed by an example of a 5-point set of 2 × 2 symmetric matrices with non-compact lamination hull. Finally, another 5-point set K is constructed, which has L (K) connected, compact and strictly smaller than Krc.

scholarly journals A remark on Gwinner's existence theorem on variational inequality problem

2000 ◽  
Vol 24 (8) ◽  
pp. 573-575
Author(s):  
V. Vetrivel ◽  
S. Nanda
Keyword(s):  
Variational Inequality ◽  
Existence Theorem ◽  
Variational Inequality Problem ◽  
Compact Convex ◽  
Inequality Problem ◽  
Upper Semicontinuous ◽  
Upper Semicontinuous Multifunction

Gwinner (1981) proved an existence theorem for a variational inequality problem involving an upper semicontinuous multifunction with compact convex values. The aim of this paper is to solve this problem for a multifunction with open inverse values.

Square Banach spaces

1969 ◽  
Vol 66 (3) ◽  
pp. 553-558 ◽  
Author(s):  
F. Cunningham
Keyword(s):  
Banach Spaces ◽  
Real Banach Space ◽  
Uniform Norm ◽  
Banach Lattices ◽  
One Dimensional ◽  
Upper Semicontinuous ◽  
Negative Function ◽  
Isometric Representation ◽  
Vector Valued Functions ◽  
Vector Valued

In (2) I described a canonical isometric representation of an arbitrary real Banach space X by vector-valued functions (with the uniform norm) on a compact Hausdorif space ω with the following properties: (1) the representing function space is invariant under multiplications by continuous real functions on ω; (2) the norm of each representing function, as a real non-negative function on ω, is upper semicontinuous; and (3) this decomposition of X is maximally fine. I called attention to the class of spaces X for which at every point of ω the component space of this representation is one-dimensional or 0, so that the representing functions are in effect real valued. I propose to call such Banach spaces square, because of the shape of the unit ball in the two-dimensional case. In (2) I stated without proof, erroneously as it turns out, that the class of square spaces coincides with what Lindenstrauss in (4) called G-spaces. The primary purpose of this paper is to show that the class of square spaces is actually properly contained in that of G-spaces. It is known ((2), p. 620, Example 1) that it contains properly the class of continuous function spaces C(ω). Among G-spaces are the M-spaces treated by Kakutani as Banach lattices (3). I shall show further that neither class, square spaces or M-spaces (regarded now purely as Banach spaces), contains the other.

Computational Micrograph Registration with Sieve Processes

1996 ◽  
Vol 54 ◽  
pp. 440-441
Author(s):  
P.J. Phillips ◽  
J. Huang ◽  
S. M. Dunn
Keyword(s):  
Planar Graph ◽  
Efficient Algorithm ◽  
Spatial Organization ◽  
Spatial Arrangement ◽  
Stereo Image ◽  
Image Model ◽  
Geometric Invariants ◽  
Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

Almost empty polygons

2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
Author(s):  
H. Nyklová
Keyword(s):  
Exact Results ◽  
Point Sets ◽  
Planar Point ◽  
Convex Position ◽  
Vertex Set ◽  
Point Set ◽  
Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

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