Abstract
In this paper, the idea of lacunary I_{lambda}-statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function. We study relations between lacunary I_{lambda}-statistical convergence with lacunary I_{lambda}-summable sequences. Moreover, we study the I_{lambda}-lacunary statistical convergence in probabilistic normed space and discuss some topological properties.
Highlights
The concept of statistical convergence [ ] which is the extended idea of convergence of real sequences has become an important tool in many branches of mathematics
We denote the class of all lacunary Iλ-statistically convergent sequences of order α defined by a Musielak-Orlicz function by SIαλ (M, θ )
If θ = ( r) and α =, is said to be Iλ-statistically convergent defined by a Musielak-Orlicz function, i.e. ∈ SIλ (M). . if Mj(x) = x, θ = ( r), λj = j, α =, Iλ-lacunary statistically convergence of order α defined by Musielak-Orlicz function reduces to I-statistical convergence
Summary
The concept of statistical convergence [ ] which is the extended idea of convergence of real sequences has become an important tool in many branches of mathematics. We call a sequence {xi}i∈N lacunary Iλ-statistically convergent of order α to M, if, for each γ > and ξ > , i We denote the class of all lacunary Iλ-statistically convergent sequences of order α defined by a Musielak-Orlicz function by SIαλ (M, θ ).
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