ASYMPTOTICALLY LACUNARY EQUIVALENT SEQUENCES DEFINED BY IDEALS AND MODULUS FUNCTION

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KUMAR VIJAY; SHARMA ARCHANA

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Journal Paper

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Journal: MATHEMATICAL SCIENCES Year:2012 | Volume:6 | Issue:- Page(s): 1-5

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Information Journal Paper

Title

ASYMPTOTICALLY LACUNARY EQUIVALENT SEQUENCES DEFINED BY IDEALS AND MODULUS FUNCTION

Author(s)

KUMAR VIJAY | SHARMA ARCHANA | Issue Writer Certificate

Keywords

STATISTICAL CONVERGENCE

I-CONVERGENCE

LACUNARY SEQUENCES

MODULUS FUNCTION

Abstract

Purpose: For a non-trivial ideal I⊂P (N), a lacunary sequence θ= (kr), and a MODULUS FUNCTION f, the purpose of present paper is to introduce certain new notions: I (f) -asymptotically equivalent, I (wf) -asymptotically equivalent, and I (Nfθ) -asymptotically equivalent sequences of numbers.Methods: We use an analytic method to obtain our results.Results: Certain theorems on generalized equivalent sequences by the use of ideals, LACUNARY SEQUENCES, and a MODULUS FUNCTION are obtained.Conclusions: We observe that if the MODULUS FUNCTION f satisfies limt ® ¥ f (t)/t>0, then the notions I (w) and I (Nθ) respectively coincide with the notions I (wf) and I (Nfθ). However, if f is bounded, the notions I (wf) and I (Nfθ) coincides respectively with the notions I (S) and I (Sθ).

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APA: Copy

KUMAR, VIJAY, & SHARMA, ARCHANA. (2012). ASYMPTOTICALLY LACUNARY EQUIVALENT SEQUENCES DEFINED BY IDEALS AND MODULUS FUNCTION. MATHEMATICAL SCIENCES, 6(-), 1-5. SID. https://sid.ir/paper/322595/en

Vancouver: Copy

KUMAR VIJAY, SHARMA ARCHANA. ASYMPTOTICALLY LACUNARY EQUIVALENT SEQUENCES DEFINED BY IDEALS AND MODULUS FUNCTION. MATHEMATICAL SCIENCES[Internet]. 2012;6(-):1-5. Available from: https://sid.ir/paper/322595/en

IEEE: Copy

VIJAY KUMAR, and ARCHANA SHARMA, “ASYMPTOTICALLY LACUNARY EQUIVALENT SEQUENCES DEFINED BY IDEALS AND MODULUS FUNCTION,” MATHEMATICAL SCIENCES, vol. 6, no. -, pp. 1–5, 2012, [Online]. Available: https://sid.ir/paper/322595/en

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