Density by Moduli and Statistical Boundedness

  title={Density by Moduli and Statistical Boundedness},
  author={Vinod Kumar Bhardwaj and Shweta Dhawan and Sandeep Gupta},
  journal={Abstract and Applied Analysis},
We have generalized the notion of statistical boundedness by introducing the concept of -statistical boundedness for scalar sequences where is an unbounded modulus. It is shown that bounded sequences are precisely those sequences which are -statistically bounded for every unbounded modulus . A decomposition theorem for -statistical convergence for vector valued sequences and a structure theorem for -statistical boundedness have also been established. 
Density by Moduli and Lacunary Statistical Convergence
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
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It is shown that, under certain conditions on a modulus f, the concepts of Wijsman lacunary strong convergence with respect to amodulus f and f-Wijs man lacunARY statistical convergence are equivalent on bounded sequences.
On Asymptotically f-statistical Equivalent Set Sequences in the Sense of Wijsman
The aim of this paper is to introduce a generalization of statistical convergence of asymptotically equivalent set sequences and examine some inclusion relations related to a new concept of Wijsman
The concept of f -statistical convergence which is, in fact, a generalization of statistical convergence, and is intermediate between the ordinary convergence and the statistical convergence, has
f-Statistical convergence of order α and strong Cesàro summability of order α with respect to a modulus
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Abstract By using modulus functions we introduce a new concept of density for sets of natural numbers. Consequently, we obtain a generalization of the notion of statistical convergence which is
On some generalizations of statistical boundedness
Fridy and Orhan (Proc. Am. Math. Soc. 125(12):3625-3631, 1997) introduced the concepts of statistical boundedness, statistical limit superior, statistical limit inferior, and they established an
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A new concept of lacunary statistical boundedness is introduced. It is shown that, for a given lacunary sequence θ={kr}, a sequence {xk} is lacunary statistical bounded if and only if for ‘almost all
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
Statistical convergence on probalistic normed spaces
In this paper we define concepts of statistical conver- gence and statistical Cauchy on probabilistic normed spaces. Then we give a useful characterization for statistically convergent sequences.
On Weak Statistical Convergence
It is shown that in a reflexive space, weak statistically Cauchy sequences are the same as weakly statistically convergent sequences.
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
Statistical limit superior and limit inferior
Following the concept of statistical convergence and statistical cluster points of a sequence x, we give a definition of statistical limit superior and inferior which yields natural relationships
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The idea of dierence sequence spaces was introduced by Kzmaz (9) and this concept was generalized by Et and C olak (5). In this paper, we introduce some new sequence spaces with respect to a modulus