Open Access

Lacunary $\mathcal{I}$-convergent and lacunary $\mathcal{I}$-bounded sequence spaces defined by a Musielak-Orlicz function over $n$-normed spaces

Abstract

In the present paper we defined $\mathcal{I}$-convergent and $\mathcal{I}$-bounded sequence spaces defined by a Musielak-Orlicz function $\mathcal{M} = (M_k)$ over $n$-normed spaces. We also make an effort to study some topological properties and prove some inclusion relation between these spaces.

Key words: $\mathcal{I}$-convergent, $\mathcal{I}$-bounded, Orlicz function, Musielak-Orlicz function, $n$-normed space, $A$-transform.

Article Information

 Title Lacunary $\mathcal{I}$-convergent and lacunary $\mathcal{I}$-bounded sequence spaces defined by a Musielak-Orlicz function over $n$-normed spaces Source Methods Funct. Anal. Topology, Vol. 24 (2018), no. 4, 370-380 Milestones Received 24/03/2017; Revised 23/11/2017 Copyright The Author(s) 2018 (CC BY-SA)

Authors Information

M. Mursaleen
Department of Mathematics, Aligarh Muslim university, Aligarh 202002, INDIA

Sunil K. Sharma
Department of mathematics, Model Institute of Engineering & Technology, Kot Bhalwal 181122, J&K, INDIA

Citation Example

M. Mursaleen and Sunil K. Sharma, Lacunary $\mathcal{I}$-convergent and lacunary $\mathcal{I}$-bounded sequence spaces defined by a Musielak-Orlicz function over $n$-normed spaces, Methods Funct. Anal. Topology 24 (2018), no. 4, 370-380.

BibTex

@article {MFAT1115,
AUTHOR = {M. Mursaleen and Sunil K. Sharma},
TITLE = {Lacunary $\mathcal{I}$-convergent and lacunary $\mathcal{I}$-bounded sequence spaces defined by a Musielak-Orlicz function over $n$-normed spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {24},
YEAR = {2018},
NUMBER = {4},
PAGES = {370-380},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=1115},
}

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