Statistically D-bounded sequences in probabilistic normed spaces

Abstract

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.

Keywords:

• probabilistic normed space
• strong statistical convergence
• strong statistically Cauchy sequence
• statistically D-bounded sequence

AMS Subject Classifications::

• 54E70
• 46S50