A Comparative Study of Ky Fan Hemicontinuity and Brezis Pseudomonotonicity of Mappings and Existence Results

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• 作者：I. Sadeqi (1)
  M. Salehi Paydar (1)
  
  1. Department of Mathematics ; Sahand University of Technology ; Tabriz ; Iran
  
• 关键词：Brezis pseudomonotonicity ; Ky Fan hemicontinuity ; Variational inequality ; 47H05 ; 58E35
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：165
• 期：2
• 页码：344-358
• 全文大小：188 KB
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  2. Brezis, H.: Inequations variationnelles associ鈥榚s 鈥榓 des op鈥榚rateurs devolution. In: Theory and Applications of Monotone Operators, pp. 249鈥?58. Proceedings of the NATO Institute, Venice (1968)
  3. Minty, GJ (1962) Monotone (non-linear) operators in Hilbert spaces. Duke Math. J. 29: pp. 341-346 CrossRef
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  8. Hadjisavvas, N, Schaible, S (1998) From scalar to vector equilibrum problems in the quasimonotone case. J. Optim. Theory Appl. 96: pp. 297-309 CrossRef
  9. Showalter, E.: Monotone Operators in Banach Space and Nonlinear Partial Differential Equations. AMS Mathematical Surveys and Monographs (1997)
  10. Giannessi, F.: Constrained Optimization and Image Space Analysis Volume 1: Separation of Sets and Optimality Conditions. Springer, Berlin (2005)
  11. Giannessi, F.: Vector Variational Inequalities and Vector Equilibrium. Kluwer, Berlin (1999)
  12. Konnov, I.: Generalized monotone equilibrium problems and variational inequalities. In: Hadjisavvas, N., Komlosi, S., Schaible, S. (Eds.) Handbook of Generalized Convexity and Generalized Monotonicity, pp. 559鈥?18. Springer, Berlin (2005)
  13. Zeidler, E (1990) Nonlinear Functional Analysis and its Applications. II/B. Nonlinear Monotone Operators. Springer, New York CrossRef
  14. Fan, K.: A minimax inequality and applications. In: Shisha, O. (ed.) Inequalities III, pp. 103鈥?13. Academic Press, New York (1972)
  15. Fan, K (1966) Application of a theorem concerning sets with convex sections. Math. Ann. 163: pp. 189-303 CrossRef
  16. Fan, K (1984) Some properties of convex sets related to fix point theorems. Math. Ann. 266: pp. 519-537 58545" target="_blank" title="It opens in new window">CrossRef
  17. Maugeri, A, Raciti, F (2009) On existence theorems for monotone and nonmonotone variational inequalities. J. Convex. Anal. 16: pp. 899-911
  18. Borwein, J, Goebel, R (2003) Notions of relative interior in Banach spaces. J. Math. Sci. 115: pp. 2542-2554 CrossRef
  19. Habil, E.D.: Double sequences and double series. Submitted to the Islamaic University Journal (2005)
  20. Ricceri, B.: Basic existence theorems for generalized variational and quasi variational inequalities. In: Giannessi, F., Maugeri, A. (eds.) Variational Inequalities and Network Equilibrium Problems (Erice, 1994), pp. 251鈥?55. Plenum Press, New York (1995)
  21. Ansari, QH, Lalitha, CS, Mehta, M (2014) Generalized Convexity, Nonsmooth Variational Inequalities and Nonsmooth Optimization. CRC Press, Taylor & Francis Group, Boca Raton, London, New York
  
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

In this paper, we give a comparison of Brezis pseudomonotonicity and Ky Fan hemicontinuity on infinite dimensional reflexive Banach spaces from the point of view of equivalence. Moreover, some existence results on variational inequalities are given, and it is shown that the solution set of variational inequality related to a Brezis pseudomonotone mapping is weakly closed and weakly compact when the mapping satisfies some coercive conditions.