Academic Journal
An intersection theorem for set-valued mappings
| العنوان: | An intersection theorem for set-valued mappings |
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| المؤلفون: | Agarwal, Ravi P., Balaj, Mircea, O'Regan, Donal |
| بيانات النشر: | Institute of Mathematics, Academy of Sciences of the Czech Republic Matematický ústav AV ČR |
| سنة النشر: | 2013 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | keyword:intersection theorem, keyword:fixed point, keyword:saddle point, keyword:equilibrium problem, keyword:complementarity problem, msc:47H04, msc:47H10, msc:49J53 |
| الوصف: | summary:Given a nonempty convex set $X$ in a locally convex Hausdorff topological vector space, a nonempty set $Y$ and two set-valued mappings $T\colon X\rightrightarrows X$, $S\colon Y\rightrightarrows X$ we prove that under suitable conditions one can find an $x\in X$ which is simultaneously a fixed point for $T$ and a common point for the family of values of $S$. Applying our intersection theorem we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0862-7940 1572-9109 |
| Relation: | mr:MR3066821; zbl:Zbl 1275.47105; reference:[1] Agarwal, R. P., Balaj, M., O'Regan, D.: Common fixed point theorems and minimax inequalities in locally convex Hausdorff topological vector spaces.Appl. Anal. 88 (2009), 1691-1699. Zbl 1223.47057, MR 2588412, 10.1080/00036810903331874; reference:[2] Aliprantis, C. D., Border, K. C.: Infinite Dimensional Analysis. A Hitchhiker's Guide. 3rd ed.Springer Berlin (2006). Zbl 1156.46001, MR 2378491; reference:[3] Ansari, Q. H., Farajzadeh, A. P., Schaible, S.: Existence of solutions of vector variational inequalities and vector complementarity problems.J. Glob. Optim. 45 (2009), 297-307. Zbl 1226.49015, MR 2539162, 10.1007/s10898-008-9375-x; reference:[4] Ansari, Q. H., Yao, J. C.: An existence result for the generalized vector equilibrium problem.Appl. Math. Lett. 12 (1999), 53-56. Zbl 1014.49008, MR 1751352, 10.1016/S0893-9659(99)00121-4; reference:[5] Balaj, M.: An intersection theorem with applications in minimax theory and equilibrium problem.J. Math. Anal. Appl. 336 (2007), 363-371. Zbl 1124.49019, MR 2348511, 10.1016/j.jmaa.2007.02.065; reference:[6] Balaj, M.: A fixed point-equilibrium theorem with applications.Bull. Belg. Math. Soc. - Simon Stevin 17 (2010), 919-928. Zbl 1213.54061, MR 2777781, 10.36045/bbms/1292334066; reference:[7] Balaj, M., O'Regan, D.: Inclusion and intersection theorems with applications in equilibrium theory in $G$-convex spaces.J. Korean Math. Soc. 47 (2010), 1017-1029. Zbl 1203.47092, MR 2723006, 10.4134/JKMS.2010.47.5.1017; reference:[8] Fan, K.: A generalization of Tychonoff's fixed point theorem.Math. Ann. 142 (1961), 305-310. Zbl 0093.36701, MR 0131268, 10.1007/BF01353421; reference:[9] Farajzadeh, A. P., Noor, M. A., Zainab, S.: Mixed quasi complementarity problems in topological vector spaces.J. Glob. Optim. 45 (2009), 229-235. Zbl 1193.90204, MR 2539158, 10.1007/s10898-008-9368-9; reference:[10] Himmelberg, C. J.: Fixed points of compact multifunctions.J. Math. Anal. Appl. 38 (1972), 205-207. Zbl 0225.54049, MR 0303368, 10.1016/0022-247X(72)90128-X; reference:[11] Jeyakumar, V., Oettli, W., Natividad, M.: A solvability theorem for a class of quasiconvex mappings with applications to optimization.J. Math. Anal. Appl. 179 (1993), 537-546. Zbl 0791.46002, MR 1249837, 10.1006/jmaa.1993.1368; reference:[12] Khan, S. A.: Generalized vector implicit quasi complementarity problems.J. Glob. Optim. 49 (2011), 695-705. Zbl 1242.90261, MR 2781983, 10.1007/s10898-010-9557-1; reference:[13] Khanh, P. Q., Quan, N. H.: Intersection theorems, coincidence theorems and maximal-element theorems in $GFC$-spaces.Optimization 59 (2010), 115-124. Zbl 1185.49007, MR 2765472, 10.1080/02331930903500324; reference:[14] Köthe, G.: Topological Vector Spaces I.Springer Berlin (1969). MR 0248498; reference:[15] Lan, K. Q.: An intersection theorem for multivalued maps and applications.Comput. Math. Appl. 48 (2004), 725-729. Zbl 1060.49016, MR 2105247, 10.1016/j.camwa.2004.03.003; reference:[16] Lee, B. S., Farajzadeh, A. P.: Generalized vector implicit complementarity problems with corresponding variational inequality problems.Appl. Math. Lett. 21 (2008), 1095-1100. Zbl 1211.90249, MR 2450657, 10.1016/j.aml.2007.12.008; reference:[17] Lu, H., Tang, D.: An intersection theorem in L-convex spaces with applications.J. Math. Anal. Appl. 312 (2005), 343-356. Zbl 1090.47045, MR 2175223, 10.1016/j.jmaa.2005.03.085 |
| الاتاحة: | http://hdl.handle.net/10338.dmlcz/143278 |
| Rights: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use |
| رقم الانضمام: | edsbas.87388FA5 |
| قاعدة البيانات: | BASE |
Full Text Finder | تدمد: | 08627940 15729109 |
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