Statistical Convergence of Double Sequences on Probabilistic Normed Spaces | Zendy

Sevda Karakuş | Zendy; Kami̇l Demi̇rci̇ | Zendy

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Statistical Convergence of Double Sequences on Probabilistic Normed Spaces

Author(s) -

Sevda Karakuş,

Kami̇l Demi̇rci̇

Publication year - 2007

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2007/14737

Subject(s) - mathematics , probabilistic logic , convergence (economics) , modes of convergence (annotated index) , sequence (biology) , cauchy sequence , cauchy distribution , cauchy's convergence test , characterization (materials science) , normed vector space , limit of a sequence , discrete mathematics , mathematical analysis , statistics , topological vector space , topological space , limit (mathematics) , free boundary problem , materials science , cauchy boundary condition , biology , economics , nanotechnology , genetics , boundary value problem , economic growth , isolated point

The concept of statistical convergence was presented by Steinhaus in 1951.This concept was extended to the double sequences by Mursaleen and Edely in2003. Karakus has recently introduced the concept of statistical convergenceof ordinary (single) sequence on probabilistic normed spaces. In this paper,we define statistical analogues of convergence and Cauchy for double sequenceson probabilistic normed spaces. Then we display an exampl e such that ourmethod of convergence is stronger than usual convergence on probabilisticnormed spaces. Also we give a useful characterization for statisticallyconvergent double sequences

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