@article{MITTAL_PRASAD_KUMAR_1991, title={ON THE $||T||\cdot C_1$ SUMMABILITY OF A SEQUENCE OF FOURIER COEFFICIENTS}, volume={22}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4566}, DOI={10.5556/j.tkjm.22.1991.4566}, abstractNote={<div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPS’; font-weight: bold;">Mohanty and Nanda </span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPSMT’;">(1959) </span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPS’; font-weight: bold;">were the first to establish a result for the $</span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">(C,</span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPS’; font-weight: bold;">1)$ i.e. $C_1$-summability of the sequence $\</span><span style="font-size: 10.000000pt; font-family: ’ArialMT’;">{n </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">B_n(x)\}$. </span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPS’; font-weight: bold;">Varshney (1959) improved the result for $</span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPS’; font-weight: bold; font-style: italic;">(N, \frac{1}{n+1}</span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPS’; font-weight: bold;"> ) \cdot C_1$  summability which was generalised by several investiga- tors such as Sharma (1970), Singh </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">(1963), </span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPS’; font-weight: bold;">Lal (1971), Khare and Singh (1988) etc. </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">In </span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPS’; font-weight: bold;">this note, we have·</span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPSMT’;">discussed $||</span><span style="font-size: 14.000000pt; font-family: ’ArialMT’;">T||\cdot </span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPS’; font-weight: bold;">C_1$-summability of the sequence $\</span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPSMT’;">{n </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">B_x(x)\}$ </span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPS’; font-weight: bold;">which includes the result due to Khare and Singh (1988). </span></p> </div> </div> </div>}, number={1}, journal={Tamkang Journal of Mathematics}, author={MITTAL, M. L. and PRASAD, G. and KUMAR, RAJESH}, year={1991}, month={Mar.}, pages={25–29} }