Abstract
This paper discussed about the proof of the fixed point theorem on the standard 2-normed spaces by using completeness. The completeness of the standard 2-normed spaces is shown by defining a new norm. Two linear independent vectors on standard 2-normed spaces are used to define the new norm, namely which has been shown to be equivalent to standard norm.
Highlights
This paper discussed about the proof of the fixed point theorem on the standard
2-normed spaces is shown by defining a new norm
namely ‖ ‖ ‖ ‖ ‖ ‖ which has been shown to be equivalent to standard norm
Summary
Ruang bernorma merupakan ruang vektor yang didalamnya terdapat fungsi norma dan memenuhi sifat-sifat ruang bernorma. Konsep tentang ruang bernorma-2 pertama kali diperkenalkan oleh Gahler pada pertengahan tahun 1960-an [7]. . Suatu fungsi bernilai riil tak negatif yang didefinisikan sebagai suatu pemetaan ‖ ‖. ‖ ‖ ‖ ‖ ‖, disebut sebagai norma-2 di , dan pasangan ‖ ‖ disebut suatu ruang bernorma-2. Salah satu topik yang banyak dikembangkan oleh peneliti adalah teorema titik tetap pada pemetaan kontaktif di ruang Banach yang dilengkapi dengan norma-2. Beberapa penelitian yang telah membahas tentang topik tersebut diantaranya Gunawan [5], Nur, [14], serta Rumlawang [17]. Pada penelitian kali ini akan membahas kembali mengenai teorema titik tetap pada pemetaan kontraktif di ruang bernorma-2 standar
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