×

A new fixed point theorem and applications. (English) Zbl 1272.54034

Summary: A new fixed point theorem is established under the setting of a generalized finitely continuous topological space (GFC-space) without the convexity structure. As applications, a weak KKM theorem and a minimax inequalities of Ky Fan type are also obtained under suitable conditions. Our results are different from known results in the literature.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Tarafdar, E., A fixed point theorem and equilibrium point of an abstract economy, Journal of Mathematical Economics, 20, 2, 211-218, (1991) · Zbl 0718.90014
[2] Lan, K. Q.; Webb, J., New fixed point theorems for a family of mappings and applications to problems on sets with convex sections, Proceedings of the American Mathematical Society, 126, 4, 1127-1132, (1998) · Zbl 0891.46004
[3] Ansari, Q. H.; Yao, J.-C., A fixed point theorem and its applications to a system of variational inequalities, Bulletin of the Australian Mathematical Society, 59, 3, 433-442, (1999) · Zbl 0944.47037
[4] Ansari, Q. H.; Idzik, A.; Yao, J.-C., Coincidence and fixed point theorems with applications, Topological Methods in Nonlinear Analysis, 15, 1, 191-202, (2000) · Zbl 1029.54047
[5] Ding, X. P.; Tan, K.-K., Fixed point theorems and equilibria of noncompact generalized games, Fixed Point Theory and Applications, 80-96, (1992), Singapore: World Sicence, Singapore · Zbl 1404.47007
[6] Ding, X. P., Continuous selection, collectively fixed points and system of coincidence theorems in product topological spaces, Acta Mathematica Sinica, 22, 6, 1629-1638, (2006) · Zbl 1117.54032
[7] Lin, L.-J.; Ansari, Q. H., Collective fixed points and maximal elements with applications to abstract economies, Journal of Mathematical Analysis and Applications, 296, 2, 455-472, (2004) · Zbl 1051.54028
[8] Khanh, P. Q.; Long, V. S. T.; Quan, N. H., Continuous selections, collectively fixed points and weak Knaster-Kuratowski-Mazurkiewicz mappings in optimization, Journal of Optimization Theory and Applications, 151, 3, 552-572, (2011) · Zbl 1244.90221
[9] Ding, X. P.; Wang, L., Fixed points, minimax inequalities and equilibria of noncompact abstract economies in FC-spaces, Nonlinear Analysis A, 69, 2, 730-746, (2008) · Zbl 1157.47037
[10] Ding, X. P., Collective fixed points, generalized games and systems of generalized quasi-variational inclusion problems in topological spaces, Nonlinear Analysis A, 73, 6, 1834-1841, (2010) · Zbl 1229.54054
[11] Yuan, G. X.-Z., KKM Theory and Applications in Nonlinear Analysis, 218, (1999), New York, NY, USA: Marcel Dekker, New York, NY, USA
[12] Balaj, M., Weakly \(G\)-KKM mappings \(, G\)-KKM property, and minimax inequalities, Journal of Mathematical Analysis and Applications, 294, 1, 237-245, (2004) · Zbl 1053.54028
[13] Balaj, M.; O’Regan, D., Weak-equilibrium problems in \(G\)-convex spaces, Rendiconti del Circolo Matematico di Palermo, 57, 1, 103-117, (2008) · Zbl 1225.54013
[14] Tang, G.-S.; Zhang, Q.-B.; Cheng, C.-Z.\(, W-G-F\)-KKM mapping, intersection theorems and minimax inequalities in FC-space, Journal of Mathematical Analysis and Applications, 334, 2, 1481-1491, (2007) · Zbl 1123.49002
[15] Hai, N. X.; Khanh, P. Q.; Quan, N. H., Some existence theorems in nonlinear analysis for mappings on GFC-spaces and applications, Nonlinear Analysis A, 71, 12, 6170-6181, (2009) · Zbl 1188.49006
[16] Khanh, P. Q.; Quan, N. H., Intersection theorems, coincidence theorems and maximal-element theorems in GFC-spaces, Optimization, 59, 1, 115-124, (2010) · Zbl 1185.49007
[17] Khanh, P. Q.; Quan, N. H., General existence theorems, alternative theorems and applications to minimax problems, Nonlinear Analysis, 72, 5, 2706-2715, (2010) · Zbl 1192.49015
[18] Park, S., Continuous selection theorems in generalized convex spaces, Numerical Functional Analysis and Optimization, 20, 5-6, 567-583, (1999) · Zbl 0931.54017
[19] Tan, K.-K., Comparison theorems on minimax inequalities, variational inequalities, and fixed point theorems, Journal of the London Mathematical Society, 28, 3, 555-562, (1983) · Zbl 0497.49010
[20] Park, S., Generalized Fan-Browder fixed point theorems and their applications, Collection of Papers Dedicated to J. G. Park, 51-77, (1989)
[21] Liu, F.-C., On a form of KKM principle and Sup Inf Sup inequalities of von Neumann and of Ky Fan type, Journal of Mathematical Analysis and Applications, 155, 2, 420-436, (1991) · Zbl 0734.47030
[22] Kim, I., KKM theorem and minimax inequalities in \(G\)-convex spaces, Nonlinear Analysis Forum, 6, 1, 135-142, (2001) · Zbl 0993.54041
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.