@article{Pehlivan_Cakar_1990, title={THE SEQUENCE SPACE $\mathcal C(p)$ AND RELATED MATRIX TRANSFORMATIONS}, volume={21}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4668}, DOI={10.5556/j.tkjm.21.1990.4668}, abstractNote={<div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">In </span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPSMT’;">this paper we define the sequence space $\mathcal C(p)$ defined in an incom</span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPSMT’;">plete seminormed space $(</span><span style="font-size: 10.000000pt; font-family: ’Arial’; font-style: italic;">X,g)$, </span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPSMT’;">namely<br>\[ \mathcal C(p) </span><span style="font-size: 12.000000pt; font-family: ’ArialMT’;">= \</span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">{(x_k) </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">\subset </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">X: \</span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">sup_{r\ge 1}g(x_k - x_{</span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">k+r})^{p_k}\to </span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPSMT’;">0, </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">k\to\infty \</span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPSMT’;">} \]</span></p> <p><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPSMT’;">where $</span><span style="font-size: 8.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">p </span><span style="font-size: 16.000000pt; font-family: ’TimesNewRomanPSMT’;">=</span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">(p_k)$ </span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPSMT’;">is a sequence of positive numbers. Then we investigated some of its fundamental properties and some of related matrix transformations. </span></p> </div> </div> </div>}, number={3}, journal={Tamkang Journal of Mathematics}, author={Pehlivan, S. and Cakar , Ö.}, year={1990}, month={Sep.}, pages={233–237} }