Related papers: Conservative inclusion of N\"orlund methods
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We introduce the $\alpha,\beta$-symmetric difference derivative and the $\alpha,\beta$-symmetric N\"orlund sum. The associated symmetric quantum calculus is developed, which can be seen as a generalization of the forward and backward…
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It is shown that if $$ \sum_{n=1}^{N}n\left|c_{n}\right|=O(N), $$ then Lebesgue summability, $(\mathrm{C},\beta)$ summability ($\beta>0$), Abel summability, Riemann summability, and $(\gamma,\kappa)$ summability ($\kappa\geq 1$) of the…