A VARIANT OF THE GENERALIZED VECTOR VARIATIONAL INEQUALITY WITH OPERATOR SOLUTIONS

- Journal title : Communications of the Korean Mathematical Society
- Volume 21, Issue 4, 2006, pp.665-673
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2006.21.4.665

Title & Authors

A VARIANT OF THE GENERALIZED VECTOR VARIATIONAL INEQUALITY WITH OPERATOR SOLUTIONS

Kum, Sang-Ho;

Kum, Sang-Ho;

Abstract

In a recent paper, Domokos and [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].

Keywords

vector variational inequality;weakly C-pseudemonotone operator;generalized hemicontinuity;Fan-Browder fixed point theorem;

Language

English

Cited by

1.

References

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