Abstract
Fridy and Orhan (Proc. Am. Math. Soc. 125(12):3625-3631, 1997) introduced the concepts of statistical boundedness, statistical limit superior, statistical limit inferior, and they established an analog of Knopp’s Core Theorem. In the present paper, we examine the concept of statistical boundedness to establish statistical analogs of various well-known results concerning boundedness and generalize the concept of statistical boundedness by introducing the concepts of statistical boundedness of order α, λ-statistical boundedness, and λ-statistical boundedness of order α.MSC:40C05, 40A05, 46A45.
Highlights
1 Introduction The idea of statistical convergence was given by Zygmund [ ] in the first edition of his monograph published in Warsaw in
In, a statistical analog of a very basic property of convergent sequences was given by Fridy and Orhan [ ] by the formal introduction of the concept of statistical boundedness as follows: ‘The real number sequence x is statistically bounded if there is a number B such that δ({k : |xk| > B}) = ’
In the fourth section of this paper, we introduce the concept of λ-statistical boundedness and prove inclusion relations between S(b), Sλ(b) and Sμ(b) under different conditions
Summary
The idea of statistical convergence was given by Zygmund [ ] in the first edition of his monograph published in Warsaw in. Generalizing the concept of statistical convergence, Çolak [ ] in introduced the concept of statistical convergence of order α by defining the α-density δα(E) of a subset E of N as follows: A sequence x = (xk) is said to be statistically convergent of order α if there is a complex number L such that lim n nα k ≤ n : |xk – L| ≥
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