Abstract
Bounded convergence results are established for sequences of convex functions of the form F(· ,0). As particular cases, one obtains convergence results for functions of the following types: F(· ,T(·)), f+g○ T, max {f,g○ T}, g○ T, f + g, max {f,g}. In the case of the sum we obtain the well-known theorem of Beer and Lucchetti as well as the recent result obtained by Eberhard and Wenczel (and reduce to that last result when the space is complete).
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