ANALISIS TITIK TETAP PADA PEMETAAN TERDOMINASI-α DI RUANG METRIK-b SEGI EMPAT
DOI:
https://doi.org/10.25077/jmua.11.3.171-180.2022Abstract
Ruang metrik-b segi empat merupakan himpunan tak kosong yang di
dalamnya dilengkapi oleh suatu pemetaan dan memenuhi tiga aksioma yaitu definitas,
simetri, dan ketaksamaan b-segi empat. Penelitian ini membahas tentang teorema titik
tetap pada pemetaan terdominasi-α di ruang metrik-b segi empat. Proses konstruksi
pembuktian melibatkan barisan Picard yang menjadi alat dalam menemukan titik tetapnya.
Contoh 3.2 pada jurnal Shoaib [10] kurang tepat, sebab tidak memenuhi semua
hipotesa pada Teorema 3.1. Oleh karena itu diberikan contoh baru dengan mendefinisikan
ulang pemetaan yang memenuhi kondisi terdominasi α sehingga semua hipotesa
pada teorema terpenuhi.
Kata Kunci: Pemetaan terdominasi, Ruang metrik-b segi empat, Titik tetap
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