Invariant means and lacunary sequence spaces of order (<i>α</i>, <i>β</i>)
M. Mursaleen, Md. Nasiruzzaman, Sunil K. Sharma, Qing‐Bo Cai
Abstract
Abstract In this article, we use the notion of lacunary statistical convergence of order <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>β</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> \left(\alpha ,\beta ) to introduce new sequence spaces by lacunary sequence, invariant means defined by Musielak-Orlicz function <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi class="MJX-tex-caligraphic" mathvariant="script">ℳ</m:mi> <m:mo>=</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>ℵ</m:mi> </m:mrow> <m:mrow> <m:mi>k</m:mi> </m:mrow> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {\mathcal{ {\mathcal M} }}=\left({\aleph }_{k}) . We also examine some topological properties and prove inclusion relations between newly constructed sequence spaces.