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Continuous selection, collectively fixed points and system of coincidence theorems in product topological spaces. (English) Zbl 1117.54032
Summary: Some new continuous selection theorems are proved in noncompact topological spaces. As applications, some new collectively fixed point theorems and coincidence theorems for two families of set-valued mappings defined on product spaces of noncompact topological spaces are obtained under very weak assumptions. These results generalize many known results in the recent literature.
MSC:
54C65Continuous selections
47H10Fixed point theorems for nonlinear operators on topological linear spaces
54H25Fixed-point and coincidence theorems in topological spaces
References:
[1]Michael, E.: Continuous selections I. Ann. of Math., 63, 361–382 (1956) · Zbl 0071.15902 · doi:10.2307/1969615
[2]Browder, F. E.: The fixed point theory of Multi-valued mappings in topological vector spaces. Math. Ann., 177, 283–301 (1968) · Zbl 0176.45204 · doi:10.1007/BF01350721
[3]Browder, F. E.: Coincidence theorems, minimax theorems, and variational inequalities. Contemporary Math., 26, 67–80 (1984)
[4]Ding, X. P.: Continuous selection theorem, coincidence theorems and intersection theorems concerning sets with H-convex sections. J. Austral Math. Soc. (Ser. A), 52, 11–25 (1992) · doi:10.1017/S1446788700032833
[5]Ding, X. P., Kim, W. K., Tan, K. K.: A Selection theorem and its applications. Bull Austral Math. Soc., 46, 205–212 (1992) · Zbl 0762.47030 · doi:10.1017/S0004972700011849
[6]Park, S.: Continuous selection theorems in generalized convex spaces. Number Funct. Anal. Optim., 25, 567–583 (1999) · Zbl 0931.54017 · doi:10.1080/01630569908816911
[7]Ding, X. P., Park, J. Y.: Continuous selection theorem, coincidence theorem, and generalized equilibrium in L-convex spaces. Comput. Math. Appl., 44, 95–103 (2002) · Zbl 1017.54012 · doi:10.1016/S0898-1221(02)00132-3
[8]Ding, X. P., Park, J. Y.: Colllectively fixed point theorem and abstract economy in G-convex spaces. Numer Funct. Anal. Optim., 23(7/8), 779–790 (2002) · Zbl 1024.54029 · doi:10.1081/NFA-120016269
[9]Yu, Z. T., Lin, L. J.: Continuous selection and fixed point theorems. Nonlinear Anal., 52(2), 445–455 (2003) · Zbl 1033.54011 · doi:10.1016/S0362-546X(02)00107-4
[10]Lin, L. J., Park, S.: On some generalized quasi-equilibrium problems. J. Math. Anal. Appl., 224(1), 167–181 (1998) · Zbl 0924.49008 · doi:10.1006/jmaa.1998.5964
[11]Tarafdar, E.: A point theorem and equilibrium point of an abstract economy. J. Math. Econom, 20(2), 211–218 (1991) · Zbl 0718.90014 · doi:10.1016/0304-4068(91)90010-Q
[12]Lan, K. Q., Webb, J.: New fixed point theorems for a family of mappings and applications to problems on sets with convex sections. Proc Amer. Math. Soc., 126(4), 1127–1132 (1998) · Zbl 0891.46004 · doi:10.1090/S0002-9939-98-04347-0
[13]Ansari, Q. H., Yao, J. C.: A fixed point theorem and its applications to a system of variational inequalities. Bull Austral Math. Soc., 59(2), 433–442 (1999) · Zbl 0944.47037 · doi:10.1017/S0004972700033116
[14]Ding, X. P., Park, J. Y.: New collevtively fixed point theorems and applications in G-convex spaces. Appl. Math. Mech., 23(11), 1237–1249 (2002) · Zbl 1036.47039 · doi:10.1007/BF02439455
[15]Ding, X. P., Park, J. Y.: Collectively fixed-point theorems in noncompact G-convex Spaces. Appl. Math. Lett., 16(3), 137–142 (2003) · Zbl 1064.47051 · doi:10.1016/S0893-9659(03)80022-8
[16]Ding, X. P.: Collectively fixed points and equilibria of generalized games with U-majorized correspondences in locally G-convex uniform spaces. J Sichuan Normal Univ., 25(6), 551–556 (2002)
[17]von Neumann, J.: Über ein ökonomsiches Gleichungssystem und eine Verallgemeinering des Browerschen Fixpunktsatzes. Ergeb. Math. Kolloq, 8, 73–83 (1937)
[18]Ding, X. P.: Coincidence theorems involving composites of acyclic mappings in contractible spaces. Appl. Math. Lett., 11(2), 85–89 (1998) · doi:10.1016/S0893-9659(98)00016-0
[19]Ding, X. P.: Coincidence theorems in topological spaces and their applications. Appl. Math. Lett., 12, 99–105 (1999) · Zbl 0942.54030 · doi:10.1016/S0893-9659(99)00108-1
[20]Ding, X. P.: Coincidence theorems and generalized equilibrium in topological spaces. Indian J. Pure. Appl. Math., 30(10), 1053–1062 (1999)
[21]Ding, X. P.: Coincidence theorems involving composites of acyclic mappings and applications. Acta. Math. Sci., 19(1), 53–61 (1999)
[22]Ding, X. P.: Coincidence theorems with applications to minimax inequalities, section theorem and best approximation in topological spaces. Nonlinear Studies, 7(2), 211–225 (2000)
[23]Deguire, P., Lassonde, M.: Familles s’electantes. Topol Methods Nonlinear Anal., 5, 261–296 (1995)
[24]Deguire, P., Tan, K. K., Yuan, G. X. Z.: The study of maximal elements, fixed point for L S -majorijed mappings and their applications to minimax and variational inequalities in product topological spaces. Nonlinear Anal., 37, 933–951 (1999) · Zbl 0930.47024 · doi:10.1016/S0362-546X(98)00084-4
[25]Ding, X. P.: Maximal elements for G B -majorized mappings in product G-convex spaces and application (II). Appl. Math. Mech., 24(6), 583–594 (2003)
[26]Lin, L. J., Yu, Z. T., Ansari, Q. H., Lai, L. P.: Fixed point and maximal theorems with applications to abstract economies and minimax in equalities. J. Math. Anal. Appl., 284(3), 636–671 (2002)
[27]Lin, L. J., Ansari, Q. H.: Collective fixed points and maximal elements with applications to abstract economies. J. Math. Anal., 296(2), 455–472 (2004) · Zbl 1051.54028 · doi:10.1016/j.jmaa.2004.03.067
[28]Ansari, Q. H., Idzik, A., Yao, J. C.: Coincidence and fixed points with applications. Topol Methods Nonlinear Anal., 15, 191–202 (2000)
[29]Lin, L. J.: System of coincidence theorems with applications. J. Math. Anal. Appl., 285(2), 408–418 (2003) · Zbl 1051.49004 · doi:10.1016/S0022-247X(03)00406-2
[30]Horvath, C. D.: Some results on multivalued mappings and inequalities without convexity, In Nonlinear and Convex Analysis, (Eds by Lin B L and Simons S), Marcel Dekker, 99–106, 1987
[31]Horvath, C. D.: Contractibility and general convexity. J. Math. Anal. Appl., 156, 341–357 (1991) · Zbl 0733.54011 · doi:10.1016/0022-247X(91)90402-L
[32]Park, S., Kim, H.: Coincidence theorems for admissible multifunctions on generalized convex spaces. J. Math. Anal. Appl., 197, 173–187 (1996) · Zbl 0851.54039 · doi:10.1006/jmaa.1996.0014
[33]Park, S., Kim, H.: Foundations of the KKM theory on generalized convex spaces. J. Math. Anal. Appl., 209, 551–571 (1997) · Zbl 0873.54048 · doi:10.1006/jmaa.1997.5388