Generalized Vector Variational and Quasi-Variational Inequalities with Operator Solutions

Authors:
Sangho Kum;Won Kyu Kim
Affiliations:
Department of Mathematics Education, Chungbuk National University, Cheongju, Korea 361-763;Department of Mathematics Education, Chungbuk National University, Cheongju, Korea 361-763
Venue:
Journal of Global Optimization
Year:
2005

Citing 4
Cited 1

Existence of solutions for a vector variational inequality: an extension of the Hartmann-Stampacchia theorem

Journal of Optimization Theory and Applications
On vector variational inequalities

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Vector variational inequality as a tool for studying vector optimization problems

Nonlinear Analysis: Theory, Methods & Applications
Variational inequalities with operator solutions

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On the Brézis Nirenberg Stampacchia-type theorems and their applications

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Abstract

In a recent paper, Domokos and Kolumbán introduced variational inequalities with operator solutions to provide a suitable unified approach to several kinds of variational inequality and vector variational inequality in Banach spaces. Inspired by their work, in this paper, we further develop the new scheme of vector variational inequalities with operator solutions from the single-valued case into the multi-valued one. We prove the existence of solutions of generalized vector variational inequalities with operator solutions and generalized quasi-vector variational inequalities with operator solutions. Some applications to generalized vector variational inequalities and generalized quasi-vector variational inequalities in a normed space are also provided.