Some highlights of our research contributions

In the first part of this exposition, one will review certain early contributions of the author in the area of Optimization and Approximation, which are of some nostalgic value to him. in the second part, one will be mostly concerned with stability and well-posedness considerations of problems in approximation theory. Specifically, the required hyperspace topologies on certain subfamilies of nonempty closed sets will be reviewed here in the context of continuity and well-posedness of the prox multifunction and the restricted center multifunction.