Abstract
The purpose of this paper is to introduce certain new sequence spaces using ideal convergence and an Orlicz function in 2-normed spaces and examine some of their properties.
Highlights
The notion of ideal convergence was introduced first by Kostyrko et al 1 as a generalization of statistical convergence which was further studied in topological spaces 2
The concept of 2-normed space was initially introduced by Gahler 5 as an interesting nonlinear generalization of a normed linear space which was subsequently studied by many authors see, 6, 7
We continue to study certain new sequence spaces by using Orlicz function and ideals in 2-normed spaces
Summary
The notion of ideal convergence was introduced first by Kostyrko et al 1 as a generalization of statistical convergence which was further studied in topological spaces 2. The concept of 2-normed space was initially introduced by Gahler 5 as an interesting nonlinear generalization of a normed linear space which was subsequently studied by many authors see, 6, 7. A lot of activities have started to study summability, sequence spaces and related topics in these nonlinear spaces see, 8–10. Recall in 11 that an Orlicz function M : 0, ∞ → 0, ∞ is continuous, convex, nondecreasing function such that M 0 0 and M x > 0 for x > 0, and M x → ∞ as x → ∞. Orlicz function was used to define sequence spaces by Parashar and Choudhary 12 and others. Note that if M is an Orlicz function M λx ≤ λM x for all λ with 0 < λ < 1
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