Some ideal-convergent generalized difference sequences in a locally convex space defined by a Musielak-Orlicz function

B. Hazarika, A. Esi
Department of Mathematics, Rajiv Gandhi University, Rono Hills, India; Department of Mathematics, Science and Art Faculty, Adiyaman University, Turkey
An ideal $I$ is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. A sequence $(x_k)$ of real numbers is said to be $I$-convergent to a real number $\ell$, if for each $ \varepsilon> 0$ the set $\{k\in \mathbb{N}\colon |x_{k}-\ell|\geq \varepsilon\}$ belongs to $I$. In this article, we introduce a new class of ideal convergent (shortly $I$-convergent) sequence spaces using %an infinite matrix, a Musielak-Orlicz function and the difference operator in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We also establish some relations between these sequence spaces.
$I$-convergence; difference space; Musielak-Orlicz function
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