Tykhonov Well-Posedness for Parametric Generalized Vector Equilibrium Problems

Panu Yimmuang, Rabian Wangkeeree

Abstract

In this paper, we introduce and analyze the notion of Tykhonov well-posedness and Tykhonov well-posedness in the general sense for parametric generalized vector equilibrium problems. Metric characterizations of well-posedness and well-posedness in the general sense are explained in terms of approximate solution sets. We consider characterizations of these well-posedness under compactness assumptions. Sufficient conditions of well-posedness in the general sense, in the form of boundedness of approximate solution sets, are investigated. Numerous examples are provided to ensure the importance of the imposed assumptions.