*(English)*Zbl 1236.46006

A new sequence space $m(M,\varphi ,q,{\Lambda})$ is defined using an Orlicz function, seminorms and $\lambda $-sequences in order to generalize the space $m\left(\varphi \right)$, introduced and studied by W.L.C. Sargent in 1960. Later on, many authors defined several other spaces in comparison with the space $m\left(\varphi \right)$. First, the author investigates the linearity, examines solidity and monotonicity and gives some inclusion results involving the spaces $m(M,\varphi ,q,{\Lambda})$. Then the relation between the space $m(M,\varphi ,q,{\Lambda})$ and the space of ${S}_{\theta}^{0}(\varphi ,{\Lambda})$-statistically convergent sequences is studied. In the last part, the relation between the space $m(M,\varphi ,q,{\Lambda})$ and the space ${m}_{\theta}^{c}(M,\varphi ,q,{\Lambda})$ of Cesàro convergence type sequences is given.

Reviewer’s remark: Certain properties like solid space, monotonicity of the space $m(M,\varphi ,q,{\Lambda})$ are investigated without any specific aim and almost all results are generalized versions of other results already studied by others.

##### MSC:

46A45 | Sequence spaces |

40A05 | Convergence and divergence of series and sequences |

40G05 | Cesàro, Euler, Nörlund and Hausdorff methods |

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