2015•Unpublished venueRequires access
KONVERGENSI-I;( I-CONVERGENCE )
Yoseph Wastu Winayaka, Atok Zulijanto
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Abstract
Statistical convergence is an extension of the convergence of a sequence of
real numbers using concept of asymptotic density. In this final project, we discuss
I-convergence as a generalization of statistical convergence. Furthermore, the
discussion is divided into two topics, namely I-convergence of a sequence in a
metric space and I-convergence of a sequence of real numbers. On the topic of
I-convergence of a sequence in a metric space we observe some properties adapted
from the convergence of the sequence in a metric space and statistical convergence.
On the topic of I-convergence of a sequence of real numbers, we present a generalization
of conditions analogous to the convergence of a sequence of real numbers,
for example I-monotone sequence, I-bounded sequence and the concept of
I-limit superior and I-limit inferior. In the end, we present the relation between
I-convergence and the concept of I-limit superior and I-limit inferior with some
counter-example to show the existence of the properties that only happen in particular
cases.