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

Article type: Research Article

Authors: Ercan, Sinan | Altinok, Hifsi | Altin, Yavuz^{; *}

Affiliations: Department of Mathematics, Fırat University, Elazığ, Turkey

Correspondence: [*] Corresponding author. Yavuz Altin, Department of Mathematics, Fı rat University, 23119, Elazı ğ, Turkey. E-mail: yaltin@firat.edu.tr.

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 Nθp(D) -summability and lacunary statistical convergence for sequences of dual numbers. We give some certain properties of these concepts and some inclusion relations.

Keywords: Statistical convergence, lacunary sequence, dual numbers

DOI: 10.3233/JIFS-181415

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 5559-5564, 2019