On lacunary statistical convergence of double sequences in credibility theory

Abstract

In 1951, the notion of statistical convergence was a more general concept than the idea of convergence as by presented by Fast. Since then statistical convergence has been was investigated by more and more researchers. On the other hand, in 2006 Li has began the survey of credibility theory and presented some convergence concepts in credibility theory. Because of the esoteric of both credibility and summability theory, the body of literature is limited. As such the only accessible notion to both theories is Pringsheim limits. The goal of this paper is to present a natural multidimensional extension of credibility theory via summability methods. To accomplish this, in this paper we present useful tools to generalize the well-known convergence definition to the concept of lacunary statistical convergence for double sequences in credibility theory. Additionally, some important results and examples will be examined.