Abstract
In this paper, we consider set optimization problems involving set relations. Using the well-known KKM-Fan Lemma and relaxed convexity assumptions, we study existence conditions for these problems. Moreover, we introduce parametric nonlinear scalarization functions for sets and study their properties. By utilizing the concerning functions, we investigate relationships between set optimization problems and equilibrium problems. Finally, sufficient conditions for the Holder continuity of solution maps to such problems via equilibrium problems are established.
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