Abstract
We generalize some sequence spaces from single to double, we study some topological properties of these double sequence spaces by using ideal convergence, difference sequence spaces, and an Orlicz function in 2-normed spaces, and we give some results related to these sequence spaces.
Highlights
The concept of I-convergent was introduced by Das et al 1 and developed by many scholars
Some new single- and double-sequence spaces defined in 2-normed spaces using ideal convergence and an Orlicz function were introduced by Savas 5, 6
Let I be an admissible ideal of N×N, M an Orlicz function, and X, ·, · a 2-normed spaces
Summary
The concept of I-convergent was introduced by Das et al 1 and developed by many scholars. C. Tripathy 2 extended the concept of I-convergence from single sequence to double sequence. Some difference double-sequence spaces and paranormed double-sequence spaces defined by Orlicz function were introduced by Tripathy and Sarma. Some new single- and double-sequence spaces defined in 2-normed spaces using ideal convergence and an Orlicz function were introduced by Savas 5, 6. Recall that an Orlicz Function, which was presented by Karasnoselskii and Rutishky. An Orlicz function M can be represented in the following integral form: M x x 0 p t dt, where p is the known kernel of. Ruckle 8 and Maddox 9 presented and discussed that if convexity of Orlicz function M is replaced by M x y ≤ M x M y this function is called Modulus function
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