GENERALIZATION OF STATISTICALLY CONVERGENT
In the late 1950's and early 1960's Kurzweil and Henstock presented the concept of Gauge integral. Following their results, Savas and Patterson extended this concept to summability theory by considering ƒ (Ψ) real valued function which is integrable in the Gauge sense on (1, ∞). The goal of this paper includes the extension of these notion to statistical convergence. This will be accomplished by presenting the definition of statistically convergent to L via cardinality in Lebesgue sense. Natural implications and variations are also presented.
Methods of Functional Analysis and Topology
Digital Object Identifier (DOI)
Rabia Savaş and Richard F. Patterson, Generalization of Statistically Convergent, Methods Funct. Anal. Topology 26 (2020), no. 4, 384-389.