On paranorm BVσ I-convergent double sequence spaces defined by an Orlicz function

What is it about?

The space BV-sigma was introduced and studied by Mursaleen. In the present article we study the double sequence spaces with the help of the space BV-sigma , an Orlicz function and the double sequence of strictly positive real numbers. We study some of its properties and prove some inclusion relations related to these new spaces.

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Why is it important?

The notion of ideal convergence is the most important development of the notion of usual convergence which played a big role for modelling uncertainty and vagueness in so many various problems in the field of science and engineering. On the other hand, the concept of BV-sigma spaces was developed, so that it became the focus of the researchers, interest. Quite recently, Vakeel Khan defined the space of all ideal convergent sequence of σ-bounded variation in space of real numbers. It was also obvious to define some new spaces of ideal convergent sequence of bounded variation by using Orlicz function and study some topological and algebraic properties and some inclusion relations of these spaces which is our aim in this article.

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