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Korovkin type theorem for sequences of operators depending on a parameter

Finta Z.

Demonstratio Mathematica

2015

Vol. 48, nr 3

391--403

We establish necessary and sufficient conditions for a parameter depending sequence (Ln,λ)n≥1 of positive linear operators such that (Ln,λ)n≥1 converges in the strong operator topology to its limit operator. Some applications of our theorem are also presented.

Oscillation criteria for second-order functional difference equation with neutral terms

Bolat Y.

Demonstratio Mathematica

2008

Vol. 41, nr 3

615-625

In this manuscript, two type of new oscillation criteria are obtained respect to coefficient ak in the following Eq. (1.1). In the subsection 2.1 considered as ak > 0. In the subsection 2.2 allowed it to be an oscillating sequence. There are no results for the oscillation of second order difference equations with oscillating coefficients up to now.