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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References

SHOWING 1-10 OF 36 REFERENCES
On pointwise and uniform statistical convergence of order α for sequences of functions
In this paper, we introduce the concepts of pointwise and uniform statistical convergence of order α for sequences of real-valued functions. Furthermore, we give the concept of an α-statistically…
LACUNARY STRONG CONVERGENCE OF DIFFERENCE SEQUENCES WITH RESPECT TO A MODULUS FUNCTION
A sequence Θ = (kr) of positive integers is called lacunary if k0 = 0, 0 < kr < kr+1 and hr = kr – kr-1 → ∞ as r → ∞. The intervals determined by Θ are denoted by Ir = (kr-1, kr]. Let ω be the set of…
On (Δm, I)-Statistical Convergence of Order α
TLDR
The concepts of (Γm, I)-statistical convergence of order α and strong (Δp m, I-Cesàro summability of orderα of real sequences are introduced and their relationship is investigated.
Statistical convergence of order α in probability
On λ-statistical convergence of order α of sequences of function
In this study we introduce the concept of Sλα(f)-statistical convergence of sequences of real valued functions. Also some relations between Sλα(f)-statistical convergence and strong…
On Strong Matrix Summability with Respect to a Modulus and Statistical Convergence
  • J. Connor
  • Philosophy, Mathematics
    Canadian Mathematical Bulletin
  • 1989
Abstract The definition of strong Cesaro summability with respect to a modulus is extended to a definition of strong A -summability with respect to a modulus when A is a nonnegative regular matrix…
Inclusions between FK spaces and Kuttner's theorem
  • I. J. Maddox
  • Mathematics, Philosophy
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1987
The result known as Kuttner's theorem [2] asserts that if 0 < p < 1 and A is a Toeplitz matrix then there is a sequence which is strongly Cesàro summable with index p but which is not A summable.…
Restricting statistical convergence
We first introduce a new notion called statistical convergence of order α and primarily show that it gives rise to a decreasing chain of closed linear subspaces of the space of all bounded real…
ON STATISTICAL CONVERGENCE
lim„ — {the number of k < n : | | > t} = 0. n These concepts are shown to be equivaleot. Also, Statistical convergence is studied as a regulär summability method, and it is shown that it cannot be…
On lacunary statistical convergence of order α
...
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