Some Classes of Ideal Convergent Sequences and Generalized Difference Matrix Operator

Abstract

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 $u=(u_k)$ of real  numbers  is said to be $B^{n}_{(m)}$-ideal convergent to a real number $\ell$ for every $\varepsilon>0,$ the set
$$\left\{k\in\mathbb{N}: |B^{n}_{(m)} u_k - \ell|\geq \varepsilon\right\}$$
belongs to $I,$ where $n,m\in\mathbb{N}.$ In this article we introduce the classes of ideal convergent sequences using a new generalized difference matrix $B^{n}_{(m)}$ and Orlicz functions and study their basic facts.   Also we investigate the different algebraic and topological properties of these classes of sequences.