Nihonkai Mathematical Journal

On Some Types of Vectoral Saddle-point Problems

Kenji Kimura
Source: Nihonkai Math. J. Volume 22, Number 1 (2011), 1-21.

Abstract

In the paper, we consider some types of vectorial saddle-point problems. We present some existence results of vectorial saddle-point problems. After that we consider a generalized vector equilibrium problem as an application.

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Primary Subjects: 49J35;
Secondary Subjects: 90A14, 91B52
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.nihmj/1339694047
Mathematical Reviews number (MathSciNet): MR2894022
Zentralblatt MATH identifier: 1246.49007

References

P. Deguire, K. K. Tan and G. X.-Z Yuan, The study of maximal elements, fixed points for $L_S$-majorized mappings and their applications to minimax and variational inequalities in product topological spaces, Nonlinear Anal., 37 (1999), 933–951.
Mathematical Reviews (MathSciNet): MR1695085
F. Ferro, A Minimax Theorem for Vector-Valued Functions, J. Optim. Theory Appl., 60(1) (1989), 19–31.
Mathematical Reviews (MathSciNet): MR981942
Digital Object Identifier: doi:10.1007/BF00938796
X. -H. Gong, The strong minimax theorem and strong saddle points of vector-valued functions, Nonlinear Anal., 68 (2008), 2228–2241.
Mathematical Reviews (MathSciNet): MR2398645
K. R. Kazmi and S. Khan, Existence of Solutions for a Vector Saddle Point Problem, Bull. Austral. Math. Soc., 61 (2000), 201–206.
Mathematical Reviews (MathSciNet): MR1748700
Zentralblatt MATH: 0946.90077
Digital Object Identifier: doi:10.1017/S0004972700022206
K. Kimura, Existence results for cone saddle points by using vector-variational-like inequalities, Nihonkai Math. J., 15(1) (2004), pp.23–32.
Mathematical Reviews (MathSciNet): MR2090134
Zentralblatt MATH: 1177.90363
Project Euclid: euclid.nihmj/1273779769
K. Kimura and T. Tanaka, Existence theorem of cone saddle-points applying a nonlinear scalarization, Taiwanese J. Math., 10(2) (2006), pp.563–571.
Mathematical Reviews (MathSciNet): MR2208286
Zentralblatt MATH: 1105.90074
L. J. Lin, Existence Theorems of Simultaneous Equilibrium Problems and Generalized Vector Quasi-Saddle Points, J. Global Optim., 32 (2005), 613–632.
Mathematical Reviews (MathSciNet): MR2191192
Digital Object Identifier: doi:10.1007/s10898-004-2697-4
Zentralblatt MATH: 1135.49009
D. T. Luc, Theory of Vector Optimization: Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin Heidelberg, 1989.
Mathematical Reviews (MathSciNet): MR1116766
M. Sion, On general minimax theorems, Pacific J. Math., 8 (1958), 171–176.
Mathematical Reviews (MathSciNet): MR97026
Zentralblatt MATH: 0081.11502
Project Euclid: euclid.pjm/1103040253
W. Takahashi, Nonlinear Functional Analysis –-Fixed Point Theory and its Applications–-, Yokohama Publishers, Yokohama, 2000.
Mathematical Reviews (MathSciNet): MR1864294
T. Tanaka, Cone-quasiconvexity of vector-valued functions, Sci. Rep. Hirosaki Univ., 42 (1995), 157–163.
Mathematical Reviews (MathSciNet): MR1356694
Zentralblatt MATH: 0836.90131
T. Tanaka, Generalized semicontinuity and existence theorems for cone saddle points, Appl. Math. Optim. 36 (1997), 313–322.
Mathematical Reviews (MathSciNet): MR1457873
Digital Object Identifier: doi:10.1007/s002459900065
Zentralblatt MATH: 0894.90132
T. Tanaka, Generalized quasiconvexities, cone saddle points, and minimax theorem for vector-valued functions, J. Optim. Theory Appl., 81(2) (1994), 355–377.
Mathematical Reviews (MathSciNet): MR1276176
Zentralblatt MATH: 0826.90102
Digital Object Identifier: doi:10.1007/BF02191669

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