×

Intersection theorems, coincidence theorems and maximal-element theorems in GFC-spaces. (English) Zbl 1185.49007

Summary: We propose a definition of GFC-spaces to encompass G-convex spaces, FC-spaces and many recent existing spaces with generalized convexity structures. Intersection, coincidence and maximal-element theorems are then established under relaxed assumptions in GFC-spaces. These results contain, as important particular cases, a number of counterparts which were recently developed in the literature.

MSC:

49J40 Variational inequalities
47H04 Set-valued operators
91B50 General equilibrium theory
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Anh LQ, Control Cyber. 36 pp 519– (2007)
[2] Border KC, Fixed-Point Theorems with Applications to Economics and Game Theory (1985) · Zbl 0558.47038
[3] Chang TH, J. Math. Anal. Appl. 203 pp 21– (1996)
[4] Deng L, J. Math. Anal. Appl. 285 pp 679– (2003) · Zbl 1039.54011
[5] Ding XP, J. Math. Anal. Appl. 266 pp 21– (2002) · Zbl 1006.47041
[6] Ding XP, Appl. Math. Mech. 24 pp 659– (2003) · Zbl 1078.47006
[7] Ding XP, Appl. Math. Mech. 24 pp 1017– (2003) · Zbl 1078.47005
[8] Ding XP, Appl. Math. Mech. 25 pp 618– (2004) · Zbl 1069.49004
[9] Ding XP, J. Math. Anal. Appl. 305 pp 29– (2005) · Zbl 1120.91001
[10] Ding XP, J. Global Optim. 36 pp 581– (2006) · Zbl 1125.54022
[11] Ding XP, J. Global Optim. 37 pp 63– (2007) · Zbl 1121.91021
[12] Ding XP, J. Global Optim. 38 pp 367– (2007) · Zbl 1176.90630
[13] Hai NX, Adv. Nonlin. Var. Inequalities 9 pp 109– (2006)
[14] DOI: 10.1007/s10957-007-9170-8 · Zbl 1146.49004
[15] DOI: 10.1007/s10957-007-9222-0 · Zbl 1126.49022
[16] DOI: 10.1007/s10898-008-9390-y · Zbl 1190.49009
[17] Khaliq A, Nonlinear Anal. 63 pp 1823– (2005) · Zbl 1224.90195
[18] DOI: 10.1007/s11228-008-0101-0 · Zbl 1161.49023
[19] DOI: 10.1007/s10898-004-2693-8 · Zbl 1097.49012
[20] Khanh PQ, Acta Math. Vietnam 34 pp 1– (2009)
[21] Khanh PQ, Nonlinear Anal. TMA 71 pp 1227– (2009) · Zbl 1176.47041
[22] Lin LJ, Bull. Austral. Math. Soc. 59 pp 481– (1999) · Zbl 0955.47037
[23] Park S, Nonlinear Anal. 30 pp 4183– (1977) · Zbl 0922.47052
[24] Park S, J. Korean Math. Soc. 37 pp 885– (2000)
[25] Park S, J. Math. Anal. Appl. 197 pp 173– (1996) · Zbl 0851.54039
[26] Park S, J. Math. Anal. Appl. 209 pp 551– (1997) · Zbl 0873.54048
[27] Park S, J. Korean Math. Soc. 36 pp 813– (1999)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.