Asymptotic Behavior of Resolvents of a Convergent Sequence of Convex Functions on Complete Geodesic Spaces

The asymptotic behavior of resolvents of a proper convex lower semicontinuous function is studied in the various settings of spaces. In this paper, we consider the asymptotic behavior of the resolvents of a sequence of functions defined in a complete geodesic space. To obtain the result, we assume the Mosco convergence of the sets of minimizers of these functions.

Automated summary

The asymptotic behavior of resolvents of a proper convex lower semicontinuous function is studied in various spaces, with a focus on the complete geodesic space and a sequence of functions. The result is obtained by assuming the Mosco convergence of sets of minimizers of these functions.