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\(\Gamma\)-inequalities and stability of generalized extremal convolutions. (English) Zbl 0738.49008

The authors prove some continuity properties of generalized infimal and supremal convolutions with respect to convergences on spaces of functions. Such properties are expressed in terms of inequality involving the \(\Gamma\)-operators introduced by E. De Giorgi and T. Franzoni.
The approach used in the paper reduces complex topological relationships to simple algebraic inequalities. Various applications are given, in particular to the continuity of the classical bilinear conjugation.
Reviewer: A.Leaci (Lecce)

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
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