A new paranormed sequence space defined by Catalan conservative matrix

Abstract

In this study, by using the Catalan conservative matrix, we define a new paranormed sequence space ℓfalse(trueC˜,pfalse) and show that the space ℓfalse(trueC˜,pfalse) is linearly isomorphic to ℓ(p). Also, we determine dual spaces and the Schauder basis of the resulting space.

A New Paranormed Sequence Space Defined by Regular Bell Matrix

“…Recently, there has been an increase in the body of literature that deals with creating new sequence spaces using a special limitation method with the help of matrix domain and researching their topological, algebraic features and matrix transformations. For instance, one can refer Alp (Alp, 2020), Altay and Başar (Altay and Başar, 2006), Aydın and Başar (Aydın and Başar, 2004), Candan (Candan, 2012), Candan and Güneş (Candan and Güneş, 2015), Choudary and Mishra (Choudary and Mishra, 1993), Dağlı (Dağlı, 2023), Dağlı and Yaying (Dağlı and Yaying, 2023), Et and Colak (Et and Colak, 1995), İlkhan et al (İlkhan et al 2019, 2020a, 2020b), Kara and Demiriz (Kara and Demiriz, 2015), Karakaya et al (Karakaya et al, 2011, 2013, Karakaya and Simsek (Karakaya and Simsek, 2012), Kirisci and Başar (Kirisci and Başar, 2010), Malkowsky (Malkowsky, 1997), , Malkowsky and Savas (Malkowsky and Savas, 2004),…”

On Some New Sequence Spaces and Their Duals

“…It is widely recognized that the metric of any linear metric space is represented by some total paranorm (see ( [1], Teorem 10.4.2, page 183)). To gain a better understanding of the theory of paranormed spaces, you can refer to these valuable articles (see Barlak [2], Zengin Alp [3], İlkhan et al [4], and many others).…”

On ideal convergence of sequences via Catalan matrix operator

“…Inquisitive readers about Catalan sequences and their properties can look further in the literature [15,18,22].…”