Kuroiwa, D., Tanaka, T. and Ha, X.T.D. (1997) On Cone Convexity of Set-Valued Maps. Nonlinear Analysis, 30, 1487-1496.
https://doi.org/10.1016/S0362-546X(97)00213-7

has been cited by the following article:

• TITLE: Continuity of Solution Mappings for Parametric Set Optimization Problems under Partial Order Relations

  AUTHORS: Yueming Sun

  KEYWORDS: Parametric Set Optimization Problem, Nonlinear Scalarization Function, Semicontinuity, Partial Order Relation

  JOURNAL NAME: Advances in Pure Mathematics, Vol.10 No.11, November 26, 2020

  ABSTRACT: This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.