Regularity characterization of asymptotically probability equivalent sequences |
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| Authors: | Richard F Patterson Ekrem Sava |
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| Institution: | aDepartment of Mathematics and Statistics, University of North Florida, 1 UNF Drive, Jacksonville, FL 32224, United States;bIstanbul Commerce University, Department of Mathematics, Uskudar, Istanbul, Turkey |
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| Abstract: | The notion of asymptotically equivalent sequences was presented by Pobyvanets in 1980. Using this definition, he presented Silverman–Toeplitz-type matrix conditions that ensure that a summability matrix preserves asymptotic equivalency. This work begins with an extension of Pobyvanets’ definition of convergence in probability. This definition is also used to present Silverman–Toeplitz-type conditions for ensuring that a summability matrix preserves asymptotic probability equivalence. In addition, we shall also present a Marouf-type characterization of such a sequence space. |
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| Keywords: | Asymptotically Equivalent sequences Regular matrix |
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