KONVERGENSI-I; ( I-CONVERGENCE )

Winayaka, Yoseph Wastu, Zulijanto, Atok

2015 | Skripsi | FMIPA UGM

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.

Kata Kunci : I-Convergence