Abstract

In this paper we define new modified generalized sine sums $K_{nr}(x)=\dfrac{1}{2\sin x}\sum_{k=1}^{n}(\triangle^{r}a_{k-1}-\triangle^{r}a_{k+1}) \tilde{S}_{k}^{r-1}(x)$ and study their $L^{1}$-convergence under a newly defined class $\bold{K}^{\alpha}$. Our results generalize the corresponding results of Kaur, Bhatia and Ram [6] and Kaur~[7].

Keywords: $L^{1}-$convergence; conjugate Cesàro means; generalized sine sums.

MSC: 42A20, 42A32

Pages:  219$-$226     

Volume  61 ,  Issue  3 ,  2009