@article{article_903988, title={Lacunary invariant statistical equivalence for double set sequences}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={71}, pages={1–12}, year={2022}, DOI={10.31801/cfsuasmas.903988}, author={Ulusu, Uğur and Dündar, Erdinç and Pancaroğlu Akın, Nimet}, keywords={Asymptotical equivalence, double lacunary sequence, invariant mean, statistical convergence, convergence in the Wijsman sense}, abstract={In this paper, we introduce the notions of asymptotical strong <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base" style="margin-right:-.001em;"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.191em;padding-bottom:.316em;padding-right:.001em;">σ </span> </span> </span> <span class="mjx-sub" style="font-size:70.7%;vertical-align:-.212em;padding-right:.071em;"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.316em;">2 </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">σ2 </span> </span>-equivalence, asymptotical <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base" style="margin-right:-.001em;"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.191em;padding-bottom:.316em;padding-right:.001em;">σ </span> </span> </span> <span class="mjx-sub" style="font-size:70.7%;vertical-align:-.212em;padding-right:.071em;"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.316em;">2 </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">σ2 </span> </span>-statistical equivalence, asymptotical lacunary strong <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base" style="margin-right:-.001em;"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.191em;padding-bottom:.316em;padding-right:.001em;">σ </span> </span> </span> <span class="mjx-sub" style="font-size:70.7%;vertical-align:-.212em;padding-right:.071em;"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.316em;">2 </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">σ2 </span> </span>-equivalence and asymptotical lacunary <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base" style="margin-right:-.001em;"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.191em;padding-bottom:.316em;padding-right:.001em;">σ </span> </span> </span> <span class="mjx-sub" style="font-size:70.7%;vertical-align:-.212em;padding-right:.071em;"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.316em;">2 </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">σ2 </span> </span>-statistical equivalence in the Wijsman sense for double set sequences. Also, we investigate some relations between these new asymptotical equivalence notions.}, number={1}, publisher={Ankara University}