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C Orhan - One of the best experts on this subject based on the ideXlab platform.

  • lacunary statistical summability
    Journal of Mathematical Analysis and Applications, 1993
    Co-Authors: J A Fridy, C Orhan
    Abstract:

    Abstract The sequence x is said to be S θ -convergent to L if for each ϵ > 0, lim r (1/ h r ){the number of k ∈ I r : | x k − L | ≥ ϵ} = 0, where θ = { k r } is an increasing sequnece of integers such that k 0 = 0, h r ≔ k r − k r − 1 → ∞ as r → ∞ and I r ≔ ( k r − 1 , k r ]. In this paper we define the S θ -analog of the Cauchy Criterion for convergence and show that tt is equivalent to S θ -convergence. Also, S θ -convergence is compared to other summability methods, and it is shown that the S θ method can not be included by any matrix method. In addition, a Tauberian theorem for S θ -convergence is given.

Shweta Dhawan - One of the best experts on this subject based on the ideXlab platform.

  • Density by Moduli and Lacunary Statistical Convergence
    Abstract and Applied Analysis, 2016
    Co-Authors: Vinod K. Bhardwaj, Shweta Dhawan
    Abstract:

    We have introduced and studied a new concept of -lacunary statistical convergence, where is an unbounded modulus. It is shown that, under certain conditions on a modulus , the concepts of lacunary strong convergence with respect to a modulus and -lacunary statistical convergence are equivalent on bounded sequences. We further characterize those for which , where and denote the sets of all -lacunary statistically convergent sequences and -statistically convergent sequences, respectively. A general description of inclusion between two arbitrary lacunary methods of -statistical convergence is given. Finally, we give an -analog of the Cauchy Criterion for convergence and a Tauberian theorem for -convergence is also proved.

J A Fridy - One of the best experts on this subject based on the ideXlab platform.

  • lacunary statistical summability
    Journal of Mathematical Analysis and Applications, 1993
    Co-Authors: J A Fridy, C Orhan
    Abstract:

    Abstract The sequence x is said to be S θ -convergent to L if for each ϵ > 0, lim r (1/ h r ){the number of k ∈ I r : | x k − L | ≥ ϵ} = 0, where θ = { k r } is an increasing sequnece of integers such that k 0 = 0, h r ≔ k r − k r − 1 → ∞ as r → ∞ and I r ≔ ( k r − 1 , k r ]. In this paper we define the S θ -analog of the Cauchy Criterion for convergence and show that tt is equivalent to S θ -convergence. Also, S θ -convergence is compared to other summability methods, and it is shown that the S θ method can not be included by any matrix method. In addition, a Tauberian theorem for S θ -convergence is given.

Vinod K. Bhardwaj - One of the best experts on this subject based on the ideXlab platform.

  • Density by Moduli and Lacunary Statistical Convergence
    Abstract and Applied Analysis, 2016
    Co-Authors: Vinod K. Bhardwaj, Shweta Dhawan
    Abstract:

    We have introduced and studied a new concept of -lacunary statistical convergence, where is an unbounded modulus. It is shown that, under certain conditions on a modulus , the concepts of lacunary strong convergence with respect to a modulus and -lacunary statistical convergence are equivalent on bounded sequences. We further characterize those for which , where and denote the sets of all -lacunary statistically convergent sequences and -statistically convergent sequences, respectively. A general description of inclusion between two arbitrary lacunary methods of -statistical convergence is given. Finally, we give an -analog of the Cauchy Criterion for convergence and a Tauberian theorem for -convergence is also proved.

Mohammed Nour A. Rabih - One of the best experts on this subject based on the ideXlab platform.

  • On Convergence Criteria for Sequences
    International Journal of Research, 2017
    Co-Authors: Mohammed Nour A. Rabih
    Abstract:

    In this paper we discuss the concept of convergence of real, complex and functions {f_n} sequences, also we discuss the concept of sub-sequences. We presented the concept of convergence criteria for the sequences. First, we presented the Cauchy Criterion for convergence, and then we presented Weierstrass M-test for convergence and its some applications.