On The Space of Asymptotically Lacunary Equivalent Sequences Obtained From an Orlicz Function

Mahmut Karakus, Tunay Bilgin

Abstract


Non-negative sequences x and y satisfying limk!1M
􀀀

xk
yk
􀀀L



= 0
for some > 0 are called M- asymptotically equivalent of multiple L,
where x = (xk) and y = (yk) . Similarly, the strong M -asymptotically
equivalence is obtained for L = 1 by using an Orlicz function M. This
study contains some new denitions and related theorems about asymp-
totically equivalent sequences by using a lacunary sequence = (kr), a
strictly positive sequence p = (pk) and an Orlicz function.


Keywords


Asymptotically equivalence, lacunary sequence, Orlicz function.

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References


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