Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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)
  • Published : 2006.10.31
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Abstract

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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References

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  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