Semicontinuity of the Approximate Solution Sets of Multivalued Quasiequilibrium Problems

Abstract

We consider two kinds of approximate solutions and approximate solution sets to multivalued quasiequilibrium problems. Sufficient conditions for the lower semicontinuity, Hausdorff lower semicontinuity, upper semicontinuity, Hausdorff upper semicontinuity, and closedness of these approximate solution sets are established. Applications in approximate quasivariational inequalities, approximate fixed points, and approximate quasioptimization problems are provided.

Keywords:

• Closedness of multifunctions
• ε-fixed points
• ε-quasioptimization problems
• ε-solutions
• Hausdorff lower and upper semicontinuity
• Lower and upper semicontinuity
• Quasiequilibrium problems
• Quasivariational inequalities

AMS Subject Classification:

• 90C31
• 49J53