Annals of Functional Analysis

The λ+r(μ)-statistical convergence

B. de Malafosse, M. Mursaleen, and V. Rakočević

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Let λ=(λn)n1 be a nondecreasing sequence of positive numbers tending to infinity such that λ1=1 and λn+1λn+1 for all n, and let In=[nλn+1,n] for n=1,2,. Then for any given nonzero sequence μ, we define by Δ+(μ) the operator that generalizes the operator of the first difference and is defined by Δ+(μ)xk=μk(xkxk+1). In this article, for any given integer r1, we deal with the λ+r(μ) -statistical convergence that generalizes in a certain sense the well-known λEr-statistical convergence. The main results consist in determining sets of sequences χ and χ of the form sξ0 satisfying χ[V,λ]0(Δ+r(μ))χ and sets κ and κ of the form sξ satisfying κ[V,λ](λ+r(μ))κ. This study is justified since the infinite matrix associated with the operator Δ+r(μ) cannot be explicitly calculated for all r.

Article information

Ann. Funct. Anal., Volume 8, Number 1 (2017), 1-15.

Received: 16 December 2015
Accepted: 14 May 2016
First available in Project Euclid: 14 October 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46A15
Secondary: 40C05: Matrix methods 40J05: Summability in abstract structures [See also 43A55, 46A35, 46B15] (should also be assigned at least one other classification number in this section)

matrix transformations operator of first-difference statistical convergence $BK$ space


de Malafosse, B.; Mursaleen, M.; Rakočević, V. The $\lambda ^{+r}(\mu )$ -statistical convergence. Ann. Funct. Anal. 8 (2017), no. 1, 1--15. doi:10.1215/20088752-3720471.

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