Fuzzy Transforms, Korovkin Theorems and the Durrmeyer Operator

In the present paper a Korovkin-type theorem is proposed for the approximation operators defined by the inverse Ftransforms. These results allow us to choose between a variety of shapes to be used as atoms of the fuzzy partitions used within the F-transform’s framework. In this way we can enlarge considerably the class of F-transforms proposed recently by I. Perfilieva. The new fuzzy partitions are shown to include, for example the Bernstein basis polynomials. The F-transform considered with the Bernstein basis polynomials as atoms of a fuzzy partition, is shown to be the classical Durrmeyer operator. Keywords—F-transform, Korovkin Theorems, Bernstein Polynomial, Durrmeyer operator.