Multiplier Sequence Spaces Defined by Statistical Summability and Orlicz-Pettis Theorem. (23rd August 2021)

• Record Type: Journal Article
• Authors: Kama, Ramazan; Altay, Bilal
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 12(2021)
• Page Start: 1410
• Page End: 1422
• Publication Date: 2021-08-23
• Subjects: Statistical convergence -- Orlicz-Pettis Theorem -- weakly unconditionally Cauchy series -- completeness; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1961803
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we introduce some new multiplier spaces related to a series ∑ i x i in a normed space X through f – statistical summability and give some characterizations of completeness and barrelledness of the spaces through weakly unconditionally Cauchy series in X and X *, respectively. We also obtain a new version of the Orlicz-Pettis theorem within the frame of the f – statistical convergence.