ANALISIS BEBERAPA TEOREMA KETUNGGALAN TITIK TETAP DI RUANG METRIK MULTIPLIKATIF (MULTIPLICATIVE METRIC SPACES)
| Main Author: | Malahayati, Malahayati |
|---|---|
| Format: | Article info application/pdf |
| Bahasa: | eng |
| Terbitan: |
Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University
, 2018
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| Online Access: |
http://jfma.math.fsm.undip.ac.id/index.php/jfma/article/view/5 http://jfma.math.fsm.undip.ac.id/index.php/jfma/article/view/5/14 |
Daftar Isi:
- Abstract. This research was conducted to analyze several theorems about fixed point uniqueness on multiplicative metric space. Firstly, the proof of fixed point uniqueness theorem on complete multiplicative metric space is analyzed with involving multiplicative continuous functions. Then, several fixed point uniqueness theorems is analyzed without involving multiplicative continuous functions. The proof of fixed point uniqueness theorem on complete multiplicative metric space with involving multiplicative continuous functions can be done without requirement of contraction multiplicative mapping. If this mapping is satisfying a condition with involving multiplicative continuous functions then it was proven that it had the unique fixed point. Furthermore, the proof of fixed point uniqueness theorem on complete multiplicative metric space without involving multiplicative continuous functions can be done by requiring the mapping is contraction. Abstrak. Penelitian ini menganalisa beberapa teorema ketunggalan titik tetap di ruang metrik multiplikatif. Pembahasan diawali dengan menganalisa pembuktian teorema ketunggalan titik tetap di ruang metrik multiplikatif lengkap dengan melibatkan bantuan fungsi kontinu multiplikatif. Selanjutnya di analisa beberapa teorema ketunggalan titik tetap tanpa melibatkan fungsi kontinu multiplikatif. Pembuktian teorema ketunggalan titik tetap di ruang metrik multiplikatif lengkap dengan bantuan fungsi kontinu multiplikatif dapat dibuktikan tanpa mensyaratkan pemetaannya kontraksi multiplikatif. Apabila pemetaan tersebut memenuhi suatu kondisi dengan bantuan suatu fungsi kontinu multiplikatif maka terbukti mempunyai titik tetap tunggal. Sedangkan Pembuktian teorema ketunggalan titik tetap di ruang metrik multiplikatif lengkap tanpa bantuan fungsi kontinu multiplikatif dibuktikan dengan mensyaratkan pemetaannya kontraksi.