Abstract
We introduce a new class of ideal convergent (shortly I-convergent) sequence spaces using an Orlicz function and difference operator of order defined over the n-normed spaces. We investigate these spaces for some linear topological structures. These investigations will enhance the acceptability of the notion of n-norm by giving a way to construct different sequence spaces with elements in n-normed spaces. We also give some relations related to these sequence spaces.
Highlights
Throughout the paper w, ∞, c, c0, and p denote the classes of all, bounded, convergent, null, and p-absolutely summable sequences of complex numbers.The notion of statistical convergence is a very useful functional tool for studying the convergence problems of numerical sequences/matrices double sequences through the concept of density
We introduce a new class of ideal convergent shortly I-convergent sequence spaces using an Orlicz function and difference operator of order s ≥ 1 defined over the n-normed spaces
We investigate these spaces for some linear topological structures. These investigations will enhance the acceptability of the notion of n-norm by giving a way to construct different sequence spaces with elements in n-normed spaces
Summary
We introduce a new class of ideal convergent shortly I-convergent sequence spaces using an Orlicz function and difference operator of order s ≥ 1 defined over the n-normed spaces. We investigate these spaces for some linear topological structures. These investigations will enhance the acceptability of the notion of n-norm by giving a way to construct different sequence spaces with elements in n-normed spaces.
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