The Experts below are selected from a list of 9126 Experts worldwide ranked by ideXlab platform
Petra Weidner - One of the best experts on this subject based on the ideXlab platform.
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Extended Domination Sets in Vector Optimization
Operations Research ’91, 1992Co-Authors: Petra WeidnerAbstract:A vector optimization problem can be given in the following form: Determine efficient elements of a feasible point set F in a Linear Topological Space Y with respect to the domination set D ⊂ Y.
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Nonconvex separation theorems and some applications in vector optimization
Journal of Optimization Theory and Applications, 1990Co-Authors: C. Gerth, Petra WeidnerAbstract:Separation theorems for an arbitrary set and a not necessarily convex set in a Linear Topological Space are proved and applied to vector optimization. Scalarization results for weakly efficient points and properly efficient points are deduced.
I. Namioka - One of the best experts on this subject based on the ideXlab platform.
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Kakutani-type fixed point theorems: A survey
Journal of Fixed Point Theory and Applications, 2011Co-Authors: I. NamiokaAbstract:A Kakutani-type fixed point theorem refers to a theorem of the following kind: Given a group or semigroup S of continuous affine transformations s : Q → Q , where Q is a nonempty compact convex subset of a Hausdorff locally convex Linear Topological Space, then under suitable conditions S has a common fixed point in Q , i.e., a point $${a \in Q}$$ such that s ( a ) = a for each $${s \in S}$$ . In 1938, Kakutani gave two conditions under each of which a common fixed point of S in Q exists. They are (1) the condition that S be a commutative semigroup, and (2) the condition that S be an equicontinuous group. The present survey discusses subsequent generalizations of Kakutani’s two theorems above.
Jian Zhong Xiao - One of the best experts on this subject based on the ideXlab platform.
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Topological degree theory and fixed point theorems in fuzzy normed Space
Fuzzy Sets and Systems, 2004Co-Authors: Jian Zhong XiaoAbstract:Abstract In this paper, the Leray–Schauder Topological degree theory is developed in a fuzzy normed Space. Since the Linear topology on this fuzzy normed Space is not necessarily locally convex, and since each Menger probabilistic normed Space can be considered as a special fuzzy normed Space, the degree theory in this paper is different from the degree theory in locally convex Linear Topological Space presented by Nagumo (Amer. J. Math. 73 (1951) 497–511), and it also is an extension of the degree theory in Menger probabilistic normed Space studied by Zhang and Chen (Appl. Math. Mech. 10(6) (1989) 477–486). Applying this degree theory, some fixed point theorems for operators are given in fuzzy normed Spaces, and some former corresponding results are extended and improved.
Liu Xiu-hong - One of the best experts on this subject based on the ideXlab platform.
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Some Results on Vector Optimization of Set-valued Maps
Journal of Qufu Normal University, 2008Co-Authors: Liu Xiu-hongAbstract:In real ordered Linear Topological Space,some optimal conditions are discussed under the condition of convexity defined by cone of set-valued maps,and some results are obtained by studying the scalar problem corresponding to the vector optimization of set-valued maps.
Liu Jim - One of the best experts on this subject based on the ideXlab platform.
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An Alternative Theorem and Its Application to the Vector Extremum Problems
Journal of Southwest China Normal University, 2006Co-Authors: Liu JimAbstract:In this paper, (u, O2)-generalized subconvexlike set-valued map is introduced, and the alternative theorem of the map is established in Linear Topological Space. Finally, using the theorem, the optimali-ty conditions for the vector extremum problems with generalized equality and inequality constraints are obtained.