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Vacca-type series for values of the generalized Euler constant function and its derivative.

Hessami Pilehrood, Khodabakhsh, Hessami Pilehrood, Tatiana (2010)

Journal of Integer Sequences [electronic only]

Variants of Karamata's Iteration Theorem

Eugene Seneta (2006)

Publications de l'Institut Mathématique

Vector series whose lacunary subseries converge

Lech Drewnowski, Iwo Labuda (2000)

Studia Mathematica

The area of research of this paper goes back to a 1930 result of H. Auerbach showing that a scalar series is (absolutely) convergent if all its zero-density subseries converge. A series $\sum_{n} x_{n}$ in a topological vector space X is called ℒ-convergent if each of its lacunary subseries $\sum_{k} x_{n_{k}}$ (i.e. those with $n_{k + 1} - n_{k} \to \infty$ ) converges. The space X is said to have the Lacunary Convergence Property, or LCP, if every ℒ-convergent series in X is convergent; in fact, it is then subseries convergent. The Zero-Density Convergence...

Vector valued paranormed statistically convergent double sequence spaces

Binod Chandra Tripathy, Bipul Sarma (2007)

Mathematica Slovaca

Vector-valued sequence space $B M C (X)$ and its properties

Qing-Ying Bu (1996)

Commentationes Mathematicae Universitatis Carolinae

In this paper, a vector topology is introduced in the vector-valued sequence space $BMC (X)$ and convergence of sequences and sequentially compact sets in $BMC (X)$ are characterized.

Vector-valued sequence spaces generated by infinite matrices.

Rath, Nandita (2001)

International Journal of Mathematics and Mathematical Sciences