Applications of the Ky fan conjecture

Authors

  • Yboon García Facultad de Ciencias, Universidad Nacional de Ingeniería, Lima, Perú
  • Wilfredo Sosa Facultad de Ciencias, Universidad Nacional de Ingeniería, Lima, Perú

DOI:

https://doi.org/10.21754/tecnia.v13i2.476

Keywords:

Ky Fan's Lemma, variational inequality, equilibrium problems, game theory

Abstract

The subject of this work is to introduce the famous Ky Fan's Lemma as an efficient tool in order to obtain existence results, for instance, variational inequality problems, equilibrium problems and game theory.

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References

[1] Ky Fan, A., "Generalization of Tychonoff's Fixed Point Theorem", Math Annalen 142, pp.305-319, 1961.

[2] Minty, G., "Monotone (Nonlinear) Operator in Hilbert Space", Duke Math. J. 29, pp. 341-346. 1962.

[3] Browder, F. E., "Nonlinear monotone operators and convex sets in Banach Spaces", Bull. Amer. Math. Soc. 71, pp. 780-785, 1965.

[4] Gudqiang Tian, "Generalizations of the FKKM theorem and the Ky Fan Minimaz Inequality". Journal of Mathematical Analysis and applications 170, pp. 457-471, 1992.

[5] Sosa Sandoval, W., "Iterative Algorithms for the abstract Equilibrium Problem, Teses de Doutorado". Instituto de Matematica Pura e Aplicada, Série F-124/2000.

[6] N. Lusem, A., Sosa, W.."New existence results for equilibrium problems". Nonlinear Analysis: Theory, Methods and Aplications 52, pp. 621-635, 2003.

[7] Hadjisavas, N. N., Schaible, "Quasimonotone Variational inequalities in Banach Spaces", Journal of Optimization, Theory and Applications 90, pp. 95-111, 1996.

[8] Crouzeix, J. P., Martínez Legaz, J. E., Volle, M., (editores) "Generalized Convexity, Generalized Monotonicity". Kluwer Academic Publishers, 1998.

[9] Dugundji, J., Granas, A., "Fixed Point Theory", 1, Monograf. Mat, vol. 61, PWN, Warszawa, 1982.

[10] Brezis, H.. "Análisis funcional y aplicaciones, Alianza Editorial", Masson, París, 1983.

[11] Dugundji, J., "Topology",

[12] Crouzeix, J. P., "Generalized Convexity and Generalized Monotonicity", Monografías del Imca, número 17.

[13] Gorniewicz, L., "Topological Fixed Point Theory of Multivalued Mappings", Kluwer Academic Publishers, 1999.

[14] Aubin, J. P., Frankowska, H., "Set-Valued Analysis, Birkhäuser", Boston, Basel, Belin, 1990.

[15] Blum, E., Oettli, W., "From optimization and variational inequalities to equilibrium problems", Math Student, 63 pp. 123-145, 1994.

[16] Flores Bazán, F., "Optimización y cálculo de variaciones sin convexidad: Una introducción", Monografías del Imca, número 15.

[17] Knaster, B., Kuratowsky, C., Mazurkiewicz, S., "Ein Beweis des Fixpunktsatzes für n- dimensionale simplexe", Fundamenta Math. 15, PP. 132-137, 1929.

[18] Fan, K., "Some properties of convex sets related to fixed point theorems", Math. Am. 266, pp. 519- 537, 1984.

[19] Fan, A., "A minimax inequality and applications", In Inequality III, edited by O. Shisha, Academic Press, New York, 103-113, 1972.

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Published

2003-12-01

How to Cite

[1]
Y. García and W. Sosa, “Applications of the Ky fan conjecture”, TECNIA, vol. 13, no. 2, Dec. 2003.

Issue

Vol. 13 No. 2 (2003)

Section

Articles

License

Copyright (c) 2003 TECNIA

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