TEOREMA TITIK TETAP DI RUANG NORM-2 (R n, k., .k2)
DOI:
https://doi.org/10.25077/jmu.10.1.116-128.2021Abstract
Pada penelitian ini akan dibahas teorema titik tetap di ruang norm-2 (Rn, k., .k2). Teorema titik tetap merupakan teorema yang menyatakan eksistensi dan ketunggalan titik tetap. Norm-2 k., .k2 didefinisikan sebagai kx, yk2 := det x · x x · y y · x y · y 1 2 dengan x, y ∈ Rn. Pasangan terurut ruang vektor Rn dengan norm-2 k., .k2 disebut ruang norm-2(Rn, k., .k2). Ruang norm-2(Rn, k., .k2) merupakan ruang banach artinya ruang norm-2(Rn, k., .k2) bersifat lengkap. Ruang norm-2(Rn, k., .k2) bersifat lengkap dibuktikan dengan cara menunjukkan ekivalensi antara norm dengan norm baru. Norm baru ini dibagun dari norm-2 k., .k2 dengan menggunakan dua vektor yang bebas linier. Teorema titik tetap menyatakan jika pemetaan T : Rn → Rn dari ruang norm-2 lengkap (Rn, k., .k2) merupakan pemetaan kontraktif maka T memiliki titik tetap yang tunggal.
Kata Kunci: Norm, Ruang norm-2, Teorema Titik Tetap.
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