Some new paranormed sequence spaces and core theorems

Abstract

Let μ ∈ { ∞ , c, c 0 }. In this study, by using lambda matrix Λ and difference matrix B, we introduce the new nonabsolute type paranormed sequence space μ(λ , B; p) and prove that μ(λ , B; p) and μ(p) linearly isomorphic. Further, we give some inclusion relations concerning the space μ(λ , B; p). Afterwards, we determine the alpha-, beta-and gamma-duals of the space μ(λ , p; B). We also give the characterization of the classes (μ(λ , B; p) : ν) and (ν : μ(λ , B; p)), where ν is any given sequence space. Moreover, we introduce the Λ-core of a complex valued sequence and determine the necessary and sufficient conditions on a matrix A for which Λ − core(Ax) ⊆ K − core(x) and Λ − core(Ax) ⊆ st − core(x) for all x ∈ ∞ .

A New Outlook for Almost Convergent Sequence Spaces

“…Building a new one using previously defined spaces is a common way of lately. Researchers interested in this subject should examine the relevant articles [5][6][7][8][9][10][11][12][13], [16], [18], c , ĉ and s ĉ , respectively, where R is defined in the previous study of Candan [2]. A full detail of the above aforementioned matrix R are important for us to work out at this time and we will just accept as valid without details the usual rules.…”

A different approach for almost sequence spaces defined by a generalized weighted means

“…Further, using generalized difference Fibonacci matrix, Candan and Kayaduman defined ̂ ( , ) space [24]. Furthermore, it can be looked at those works about this topic nearly: [9], [10], [11], [25], [26], [27], [28], [29], [30], [31]…”

“…Theorem 11: Assume that the entries of the infinite matrices = ( ) and = ( ) are connected with the relation = , (11), for all , ∈ and be any given sequence space. Then, ∈ ( : ( , )) necessary and sufficient condition ∈ ( : ).…”