Some novel approaches on the (\overline{N},p,q) summability of double sequences of fuzzy numbers and its applications

In this paper, our aim is to make a novel interpretation of relation between (\overline{N},p,q) method and P-convergence for double sequences of fuzzy numbers. In accordance with this aim, we derive some Tauberian conditions, controlling O-oscillatory behavior of a double sequence of fuzzy numbers in certain senses, from (\overline{N},p,q) summability to P- convergence with some restrictions on the weight sequences. As special cases, we indicate that O-condition of Hardy type with respect to (P_m) and (Q_n) are Tauberian conditions for (\overline{N},p,q) summability under some additional conditions. In the sequel, we prove a fuzzy Korovkin-type approximation theorem by using the (\overline{N},p,q) summability method for fuzzy positive linear operators.

Some novel approaches on the (\overline{N},p,q) summability of double sequences of fuzzy numbers and its applications Keywords:

Double sequences of fuzzy numbers , convergence in Pringsheim's sense , (\overline{N} , P , q) summability , regularly varying sequences , slowly decreasing sequences , slowly oscillating sequences , weighted mean summability method , fuzzy Korovkin theory