Asymptotically double lacunry equivalent sequences defined by Orlicz functions

This paper presents the following definition which is natural combition of the definition for asymptotically equivalent and Orlicz function. The two nonnegative double sequences x=(x_{k,l}) and y=(y_{k,l}) are said to be M-asymptotically double equivalent to multiple L provided that for every ε&...

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Bibliographic Details
Author: Esi, Ayhan
Format: article
Status:Published version
Publication Date:2014
Country:Brasil
Institution:Universidade Estadual de Maringá (UEM)
Repository:Acta scientiarum. Technology (Online)
Language:English
OAI Identifier:oai:periodicos.uem.br/ojs:article/16391
Online Access:http://www.periodicos.uem.br/ojs/index.php/ActaSciTechnol/article/view/16391
Access Level:Open access
Keyword:asymptotically equivalence
double sequences
P-convergent
double lacunary sequence
40A99
40A05
40B05
Description
Summary:This paper presents the following definition which is natural combition of the definition for asymptotically equivalent and Orlicz function. The two nonnegative double sequences x=(x_{k,l}) and y=(y_{k,l}) are said to be M-asymptotically double equivalent to multiple L provided that for every ε>0, P-lim_{k,l}M(((|((x_{k,l})/(y_{k,l}))-L|)/ρ))=0, for some ρ>0, (denoted by x∽y) and simply M-asymptotically double equivalent if L=1. Also we give some new concepts related to this definition and some inclusion theorems.