On lacunary statistical boundedness View Full Text


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Article Info

DATE

2014-08-21

AUTHORS

Vinod K Bhardwaj, Sandeep Gupta, Syed A Mohiuddine, Adem Kılıçman

ABSTRACT

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 k w.r.t. θ’, the values xk coincide with those of a bounded sequence. Apart from studying various algebraic properties and computing the Köthe-Toeplitz duals of the space Sθ(b) of all lacunary statistical bounded sequences, a decomposition theorem is also established. We characterize those θ for which Sθ(b)=S(b). Finally, we give a general description of inclusion between two arbitrary lacunary methods of statistical boundedness.MSC:40C05, 40A05, 46A45. More... »

PAGES

311

References to SciGraph publications

  • 2013-07-03. A new variant of statistical convergence in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2013-04-23. On λ-statistical convergence of order α of sequences of function in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2013-02-18. On pointwise and uniform statistical convergence of order α for sequences of functions in FIXED POINT THEORY AND ALGORITHMS FOR SCIENCES AND ENGINEERING
  • 2014-01-09. On some generalizations of statistical boundedness in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2004-06-01. On a Class of Generalized Lacunary Difference Sequence Spaces Defined by Orlicz Functions in ACTA MATHEMATICAE APPLICATAE SINICA, ENGLISH SERIES
  • 2013-03-21. Statistical convergence through de la Vallée-Poussin mean in locally solid Riesz spaces in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2012-10-09. Statistical summability through a lacunary sequence in locally solid Riesz spaces in JOURNAL OF INEQUALITIES AND APPLICATIONS
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