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Statistically D-bounded sequences in probabilistic normed spaces

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In this study, the concept of a statistically D-bounded sequence in a probabilistic normed (PN) space endowed with the strong topology is introduced and its basic properties are investigated. It is shown that a strongly statistically convergent sequence and a strong statistically Cauchy sequence are statistically D-bounded under certain conditions. A sequence which goes far away from the limit point infinitely many times and presents random deviations in a PN space may be handled with the tools of strong statistical convergence and statistical D-boundedness.
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Keywords: probabilistic normed space; statistically D-bounded sequence; strong statistical convergence; strong statistically Cauchy sequence

Document Type: Research Article

Affiliations: 1: Faculty of Arts and Sciences, Department of Mathematics, Mehmet Akif Ersoy University, Burdur, Turkey 2: Faculty of Arts and Sciences, Department of Mathematics, Suleyman Demirel University, Isparta, Turkey

Publication date: 2009-08-01

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