Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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ON OPTIMAL SOLUTIONS OF WELL-POSED PROBLEMS AND VARIATIONAL INEQUALITIES

  • Ram, Tirth (Department of Mathematics, University of Jammu) ;
  • Kim, Jong Kyu (Department of Mathematics Education, Kyungnam University) ;
  • Kour, Ravdeep (Department of Mathematics, University of Jammu)
  • Received : 2021.05.15
  • Accepted : 2021.08.15
  • Published : 2021.12.15
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Abstract

In this paper, we study well-posed problems and variational inequalities in locally convex Hausdorff topological vector spaces. The necessary and sufficient conditions are obtained for the existence of solutions of variational inequality problems and quasi variational inequalities even when the underlying set K is not convex. In certain cases, solutions obtained are not unique. Moreover, counter examples are also presented for the authenticity of the main results.

Keywords

Acknowledgement

This work was supported by the Basic Science Research Program through the National Research Foundation(NRF) Grant funded by Ministry of Education of the republic of Korea (2018R1D1A1B07045427).

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