f-Statistical convergence of order α and strong Cesàro summability of order α with respect to a modulus

@article{Bhardwaj2015fStatisticalCO,
  title={f-Statistical convergence of order $\alpha$ and strong Ces{\`a}ro summability of order $\alpha$ with respect to a modulus},
  author={Vinod Kumar Bhardwaj and Shweta Dhawan},
  journal={Journal of Inequalities and Applications},
  year={2015},
  volume={2015},
  pages={1-14}
}
In this paper, following a very recent and new approach of Aizpuru et al. (Quaest. Math. 37:525-530, 2014), we further generalize a concept of α-density to that of fα$f_{\alpha}$-density, where f is an unbounded modulus and 0<α≤1$0 < \alpha\leq1$. As a consequence, we obtain a new nonmatrix convergence method, namely f-statistical convergence of order α or Sαf$S_{\alpha}^{f}$-convergence, which is intermediate between the ordinary convergence and the statistical convergence of order α. We also… 
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