F-Statistical Convergence of Double Sequences of Order $$\widetilde{\alpha }$$

Abstract

In this paper, we present new concepts of f-statistical convergence for double sequences of order $$ \widetilde{\alpha }$$ and strong f-Cesaro summability for double sequences of order $$ \widetilde{\alpha }$$ for sequences of (complex or real) numbers. Besides, we give the relationship between the spaces $$ w_{\tilde{\alpha },0} ^{2}\left( f\right) , w_{\tilde{\alpha }}^{2}\left( f\right) $$ and $$ w_{\tilde{\alpha },\infty }^{2}\left( f\right) $$ . Furthermore, we express the properties of the strong f-Cesaro summability of order $$ \widetilde{\beta }$$ which is related to strong f-Cesaro summability of order $$ \tilde{\alpha }$$ . Also some relations between f-statistical convergence of order $$ \widetilde{\alpha }$$ and strong f-Cesaro summability of order $$ \widetilde{\alpha }$$ are given. The main purpose of this paper is to introduce and examine the concept of f-double statistical convergence of order $$ \widetilde{\alpha },$$ where f-is an unbounded function and give relations between f-double statistical convergence of order $$ \widetilde{\alpha }$$ and strong f-Cesaro summability for double sequence of order $$ \widetilde{\alpha }$$ so as to fill up the existing gaps in the literature.