Lacunary statistical convergence and inclusion properties between lacunary methods

By Jinlu Li. 2000

58 citations recorded by the source corpus.

A lacunary sequence is an increasing integer sequence θ={kr} such that kr−kr−1→∞ as r→∞. A sequence x is called sθ-convergent to L provided that for each ϵ>0, limr(1/(kr−kr−1)){the number of   kr−1<k≤kr:|xk−L|≥ϵ}=0. In this paper, we study the general description of inclusion between two arbitrary lacunary sequences convergent.

Subfields: Algebra and Number Theory, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/64a657f5530dab0e7ddcdb8019510ebb608e9782

How researchers see this paper

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In Algebra and Number Theory

1. Ekrem Savas
2. Richard F. Patterson

In Numerical Analysis

1. Pratulananda Das
2. Sumit Som
3. Sanjoy Kr. Ghosal
4. Ekrem Savas
5. Richard F. Patterson

In Statistics and Probability

1. Ekrem Savas
2. Pratulananda Das
3. Sumit Som
4. Sanjoy Kr. Ghosal
5. Richard F. Patterson

Citations in the corpus

• Lacunary statistical convergence of double sequences (2005, background): “✷ The following theorems are multidimensional analogues of some results of Li [7].”
• Statistical convergence of order α in probability (2015, background): “Some of the most important concepts introduced are : lacunary statistical convergence by Fridy & Orhan [18] (for more results on this convergence see the paper of Li [24]), I-convergence by Kostyrko et al.”