Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.4.2020.2.03
Volume 4, Issue 2, 1 August 2020, Pages 189-206

 

Abstract. Since its appearance, even convexity has become a remarkable notion in convex analysis. In the fifties, W. Fenchel introduced the evenly convex sets as those sets solving linear systems containing strict inequalities. Later on, in the eighties, evenly quasiconvex functions were introduced as those whose sublevel sets are evenly convex. The significance of even convexity relies on the different areas where it enjoys applications, ranging from convex optimization to microeconomics. In this paper, we review some of the main properties of evenly convex sets and evenly quasiconvex functions, provide further characterizations of evenly convex sets, and present some new results for evenly quasiconvex functions.

 

How to Cite this Article:
Miguel A. Goberna, Margarita M.L. Rodríguez, José Vicente-Pérez, Evenly convex sets, and evenly quasiconvex functions, revisited, J. Nonlinear Var. Anal. 4 (2020), 189-206.