대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제21권4호
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  • Pages.665-673
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  • 2006
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A VARIANT OF THE GENERALIZED VECTOR VARIATIONAL INEQUALITY WITH OPERATOR SOLUTIONS

  • Kum, Sang-Ho (Department of Mathematics Education Chungbuk National University)
  • 발행 : 2006.10.31
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초록

In a recent paper, Domokos and $Kolumb\'{a}}n$ [2] gave an interesting interpretation of variational inequalities (VI) and vector variational inequalities (VVI) in Banach space settings in terms of variational inequalities with operator solutions (in short, OVVI). Inspired by their work, in a former paper [4], we proposed the scheme of generalized vector variational inequality with operator solutions (in short, GOVVI) which extends (OVVI) into a multivalued case. In this note, we further develop the previous work [4]. A more general pseudomonotone operator is treated. We present a result on the existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [8] within the framework of (GOVVI) by exploiting some techniques on (GOVVI) or (GVVI) in [4].

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참고문헌

  1. F. E. Browder, The fixed point theory of multivalued mappings in topological vector space, Math. Ann. 177 (1968), 283-30l https://doi.org/10.1007/BF01350721
  2. A. Domokos and J. Kolumban, Variational inequalities with operator solutions, J. Global Optim. 23 (2002), 99-110 https://doi.org/10.1023/A:1014096127736
  3. I. V. Konnov and J. C. Yao, On the generalized vector variational inequality problem, J. Math. Anal. Appl. 206 (1997), 42-58 https://doi.org/10.1006/jmaa.1997.5192
  4. S. H. Kum and W. K. Kim, Generalized vector variational and quasi-variational inequalities with operator solutions, J. Global Optim. 32 (2005), 581-595 https://doi.org/10.1007/s10898-004-2695-6
  5. G. M. Lee and S. H. Kum, On implicit vector variational inequalities, J. Optim. Theory Appl. 104 (2000), 409-425 https://doi.org/10.1023/A:1004617914993
  6. S. Park, Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps, J. Korean Math. Soc. 31 (1994), 493-519
  7. W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1974
  8. S. J. Yu and J. C. Yao, On vector variational inequalities, J. Optim. Theory Appl. 89 (1996), 749-769 https://doi.org/10.1007/BF02275358

피인용 문헌

  1. On generalized operator quasi-equilibrium problems vol.345, pp.1, 2008, https://doi.org/10.1016/j.jmaa.2008.04.035
  2. Semicontinuity of the solution multifunctions of the parametric generalized operator equilibrium problems vol.71, pp.12, 2009, https://doi.org/10.1016/j.na.2009.04.036
  3. Applications of some basic theorems in the KKM theory vol.2011, pp.1, 2011, https://doi.org/10.1186/1687-1812-2011-98