Compact Matrix Operators on Absolute Cesàro Spaces

A New Paranormed Series Space and Matrix Transformations

“…Moreover, some new sequence and series spaces have been examined by various authors in [9][10][11][12][13]15,23,28]. At this point, space |C α | p for α > −1 and 1 ≤ p < ∞, as the set of all series summable by the method |C, α| p defined by Flett in [6], has been defined and studied in [23] .…”

Applications of Measure of Noncompactness in the Series Spaces of Generalized Absolute Cesàro Means

“…One of the research areas in the theory of summability is absolute summability factors and comparison of the methods, which plays an important role in Fourier Analysis and approximation theory and has been widely studied by many authors in the literature (Borwein, 1958;Çanak, 2020;Das, 1970;Flett, 1957;Hazar and Sarıgöl, 2018a, b;Mazhar, 1971;Mehdi, 1960;Mohapatra and Sarıgöl, 2018;Nur and Gunawan, 2019;Sarıgöl, 2015Sarıgöl, , 2016Sezer and Çanak, 2015). Recently, independently of these topics, some sequence spaces have been generated and examined by several authors (Altay and Başar, 2007;Altay et al, 2009;Başarır and Kara, 2011a,b, 2012a,b, 2013Et and Işık, 2012;Hazar, 2020;İlkhan and Kara, 2019;İlkhan, 2020;Kara and İlkhan, 2016;Kara and Başarır, 2011;Karakaya et al, 2011;Sarıgöl, 2016;Zengin Alp and İlkhan, 2019).…”