Lacunary statistical convergence and strongly lacunary summable for sequences of dual numbers

Abstract

Dual number algebra is a powerful mathematical tool for the kinematic and dynamic analysis of spatial mechanisms. The algebra of dual numbers has been originally conceived by Clifford [1], but its first applications to mechanics are due to Kotelnikov [2] and Study [3]. In this paper, we focus on summability of sequences of dual numbers. We introduce the concepts of strongly N-theta(P)(ID)-summability and lacunary statistical convergence for sequences of dual numbers. We give some certain properties of these concepts and some inclusion relations.