zbMATH — the first resource for mathematics

Existence and stability of solutions for generalized ky Fan inequality problems with trifunctions. (English) Zbl 1229.90266
An existence theorem is given for solutions to a generalized Ky Fan inequality formulated over locally convex Hausdorff topological linear spaces. The theorem is obtained by applying the Kakutani-Fan-Glicksberg fixed-point theorem without imposing the condition that the dual of the ordering cone has a weak* compact base. Several applications of the existence theorem and a stability result for the solution set are also given.

90C48 Programming in abstract spaces
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
47H10 Fixed-point theorems
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
49J27 Existence theories for problems in abstract spaces
Full Text: DOI
[1] Fan, K.: A minimax inequality and applications. In: Shihsha, O. (ed.) Inequality III, pp. 103–113. Academic Press, New York (1972) · Zbl 0302.49019
[2] Brezis, H., Nirenberg, L., Stampacchia, G.: A remark on Ky Fan’s minimax principle. Boll. Unione Mat. Ital. (III) VI, 129–132 (1972) · Zbl 0264.49013
[3] Fu, J.Y.: Generalized vector quasi-equilibrium problems. Math. Methods Oper. Res. 52, 57–64 (2000) · Zbl 1054.90068 · doi:10.1007/s001860000058
[4] Tan, N.X.: On the existence of solutions of quasivariational inclusion problems. J. Optim. Theory Appl. 123, 619–638 (2004) · Zbl 1059.49020 · doi:10.1007/s10957-004-5726-z
[5] Jeyakumar, V., Oettle, W., Natividad, M.: A solvability theorem for a class of quasi-convex mappings with applications to optimization. J. Math. Anal. Appl. 197, 537–546 (1993) · Zbl 0791.46002 · doi:10.1006/jmaa.1993.1368
[6] Jameson, G.: Ordered Linear Spaces. Lecture Notes in Mathematics, vol. 141. Springer, Berlin (1970) · Zbl 0196.13401
[7] Aubin, J.P., Ekeland, I.: Applied Nonlinear Analysis. Wiley, New York (1984) · Zbl 0641.47066
[8] Hou, S.H.: On property (Q) and other semicontinuity properties of multifunctions. Pac. J. Math. 103, 39–56 (1982) · Zbl 0451.54015
[9] Luc, D.T.: Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems, vol. 319. Springer, New York (1989) · Zbl 0688.90051
[10] Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis, 2nd edn. Springer, Berlin (1999) · Zbl 0938.46001
[11] Ferro, F.: A minimax theorem for vector-valued functions. J. Optim. Theory Appl. 60, 19–31 (1989) · Zbl 0631.90077 · doi:10.1007/BF00938796
[12] Schaefer, H.H.: Topological Vector Spaces. Springer, New York (1980) · Zbl 0435.46003
[13] Holmes, R.B.: Geometric Functional Analysis and Its Applications. Springer, New York (1975) · Zbl 0336.46001
[14] Yu, J.: Essential weak efficient solution in multiobjective optimization problems. J. Math. Anal. Appl. 166, 230–235 (1992) · Zbl 0753.90058 · doi:10.1016/0022-247X(92)90338-E
[15] Isac, G., Yuan, X.Z.: The existence of essentially connected components of solutions for variational inequalities. In: Giannessi, F. (ed.) Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, pp. 253–265. Kluwer, Dordrecht (2000) · Zbl 0978.47051
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.