Characterization of some matrix classes involving some sets with speed

Abstract

The paper introduces the notions of boundedness and convergence with speed for difference sequences, and characterizes certain matrix classes associating the sets of such classes of sequences involving the operator and two speeds D. k / and D. k / .0 < k % 1; 0 < k % 1/. The results obtained in this paper should easily extendible to difference sequences of higher orders, and even, in combination with multipliers.