Nonlinear scalarizing functions in set optimization problems. (2nd September 2019) - Han, Yu
Abstract : In this paper, we obtain Hölder continuity of the nonlinear scalarizing function for l -type less order relation, which is introduced by Hernández and Rodríguez-Marín (J. Math. Anal. Appl. 2007;325:1–18). Moreover, we introduce the nonlinear scalarizing function for u -type less order relation and establish continuity, convexity and Hölder continuity of the nonlinear scalarizing function for u -type less order relation. As applications, we firstly obtain Lipschitz continuity of solution mapping to the parametric equilibrium problems and then establish Lipschitz continuity of strongly approximate solution mappings for l -type less order relation, u -type less order relation and set less order relation to the parametric set optimization problems by using convexity and Hölder continuity of the nonlinear scalarizing functions.