Journal of Advances in Applied Mathematics
Quasi-equilibrium Problems and Fixed Point Theorems of the Product Mapping of Lower and Upper Semicontinuous Mappings
Download PDF (562.6 KB) PP. 89 - 100 Pub. Date: March 23, 2017
Author(s)
- Nguyen Xuan Tan*
Institute of Mathematics, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam - Nguyen Quynh Hoa
University of economics and business administration of Thai Nguyen
Abstract
Keywords
References
[1] L. Brouwer, “Ueber abbildingen von mannigfaltigkeiten,” Math. Ann., vol. 71, pp. 97 – 115, 1911.
[2] Schauder, “Der fixpunktsatz in funktionalraeumen,” Studia Math., vol. 2, pp. 171 – 180, 1934.
[3] S. Kakutani, “A generalization of brouwer’ fixed point theorem,” Duke Math. Journal, vol. 8, pp. 457 – 459, 1941.
[4] K. Fan, “A generalization of tychonoff’s fixed point theorem,” Math. ann., vol. 142, pp. 305 – 310, 1961.
[5] F. E. Browder, “The fixed point theory of multi-valued mappings in topological vector spaces,” Math. Ann., vol. 177, pp. 283–301, 1968.
[6] N. C. Yannelis and N. D. Prabhakar, “Existence of maximal elements and equilibria in linear topological spaces,” J. Math. Economics, vol. 233, pp. 233 – 245, 1983.
[7] H. Ben-El-Mechaiekh, “Fixed points for compact set-valued maps, questions answers gen,” Topology, vol. 10, pp. 153 – 156, 1992.
[8] W. K. K. X. P. Ding and K. K. Tan, “A selection theorem and its applications,” Bull. Austra. Math. Soc., vol. 46, pp. 205 – 212, 1992.
[9] C. D. Horvath, “Existension and selection theorems in topological vector spaces with a generalized convexity structure,” Ann. Fac. Sci., Toulouse, vol. 2, pp. 253 – 269, 1993.
[10] X. Wu, “A new fixed point theorem and its applications,” Proc. Amer. Math. Soc., vol. 125, pp. 1779 – 1783, 1997.
[11] S. Park, “Continuous selection theorems in generalized convex spaces,” Numer. Funct. Anal. Optim.l, vol. 25, pp. 567 – 583, 1999.
[12] Z. T. Yu and L. J. Lin, “Continuous selection and fixed point theorems,” Nonlinear Anal., vol. 52, pp. 445 – 455, 2003.
[13] T. T. T. Duong and N. X. Tan, “On the existence of solutions to generalized quasi-equilibrium problems of type i and related problems,” Ad. in Nonlinear Variational Inequalities, vol. 13, pp. 29 – 47, 2010.
[14] ——, “On the existence of solutions to generalized quasi-equilibrium problems of type ii and related problems,” Acta Math. Vietnamica, vol. 36, pp. 29 – 47, 2011.
[15] N. X. Tan, “On the existence of solutions of quasi-variational inclusion problems,” Jour. of Opt. Theory and Appl., vol. 123, pp. 619–638, 2004.
[16] W. Rudin, Principles of Mathematical Analysis. McGraw-hill, 1987.
[17] M.Sion, “On general minimax theorems,” Pacific J. Math., vol. 8, p. 171 aAS176, 1958.