### Γ-CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS, AND MINIMIZERS

Ozer Talo, Yurdal Sever

DOI Number
https://doi.org/10.22190/FUMI230521050T
First page
771
Last page
791

#### Abstract

In the present paper, we introduce the concept of Γ-convergence of a double sequence of functions defined from a metric space into real numbers. This convergence is useful as it is a convenient concept of convergence for approximating minimization problems in the field of mathematical optimization. First, we compare this convergence with pointwise and uniform convergence and obtain some properties of Γ-convergence. Later we deal with the problem of minimization. We prove that, under some additional assumptions, the Γ-convergence of a double sequence (f_{kl}) to a function f implies the convergence of the minimum values of f_{kl} to the minimum value of f. Moreover, we prove that each limit point of the double sequence of the minimizers of f_{kl} is a minimizer of f.

#### Keywords

Double sequence of functions, Pringsheim convergence, Set-valued function, Kuratowski convergence, Gamma-convergence, Minimizers.

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DOI: https://doi.org/10.22190/FUMI230521050T

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