Abstract
Let $p := \{p_j\}_{j=0}^{\infty}$ and $q := \{q_k\}_{k=0}^{\infty}$ be complex sequences with $p,q \in$ SVA. Assume that $\{s_{mn}\}_{m,n=0}^\infty$ is a double sequence in $\mathbf{C}$ (or one of $\mathbf{R}$, a Banach space, and an ordered linear space), with $s_{mn} \stackrel{st}{\rightarrow} s \hspace{6 pt} (\bar{\mathrm{N}},p,q;\alpha,\beta)$, where $(\alpha,\beta) = (1,1)$, $(1,0)$ or $(0,1)$. We give sufficient and/or necessary conditions under which $s_{mn} \stackrel{st}{\rightarrow} s$. The theory developed here is the statistical version of the work of Chen and Hsu in [Anal. Math. 26 (2000), 243-262]. Our results generalize Móricz, [J. Math. Anal. Appl. 286 (2003), 340-350].
Citation
Chang-Pao Chen. Chi-Tung Chang. "TAUBERIAN THEOREMS IN THE STATISTICAL SENSE FOR THE WEIGHTED MEANS OF DOUBLE SEQUENCES." Taiwanese J. Math. 11 (5) 1327 - 1342, 2007. https://doi.org/10.11650/twjm/1500404867
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