Adipradana, Dimaz Wisnu (2017) Pemetaan Kontraktif Pada Ruang Type-Metrik Lengkap. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Salah satu topik yang dipelajari dalam analisis fungsional
adalah ruang metrik. Konsep ruang metrik dapat diperluas,
dengan menggunakan sifat dari cone menjadi ruang metrik
cone dan juga ruang type-metrik. Konsep ruang type-metrik
berbeda dengan konsep ruang metrik. Perbedaannya terletak
pada pertidaksamaan di ruang metrik dan ruang type-metrik.
Diberikan analogi mengenai barisan konvergen dan Cauchy di
ruang type-metrik, lalu dikonstruksi contoh ruang type-metrik
dari ruang metrik cone. Pada prinsip kontraksi di ruang
type-metrik diberikan sifat Lipschitz yang digunakan untuk
menjamin keberadaan dan ketunggalan titik tetap. Dengan
menggunakan teorema titik tetap, diperoleh titik tetap tunggal
pada ruang type-metrik lengkap.
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One of the topics studied in functional analysis is the
metric space. The concept of metric space can be expanded,
using the property of the cone into the cone metric space
and also the type-metric space. The concept of a type-metric
space is different from the concept of a metric space. The
difference lies in the inequality in the metric space and the type-metric space. Given an analogy of the convergent and Cauchy sequences in the type-metric space, then constructed an example of a metric-type space of the cone metric space. On the principle of contraction in the type-metric space is given the Lipschitzian properties used to assure the existence and unity of fixed points. Using the fixed-point theorem, a single-fixed point is obtained in the complete type-metric space
| Item Type: | Thesis (Undergraduate) |
|---|---|
| Additional Information: | RSMa 514.325 Adi p |
| Uncontrolled Keywords: | ruang metrik; ruang type-metrik; ruang metrik cone; titik tetap; pemetaan kontraktif; metric space; type-metric space; cone metric space; fixed point; contractive mapping |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Mathematics and Science > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Dimaz Wisnu Adipradana |
| Date Deposited: | 19 Jan 2018 04:10 |
| Last Modified: | 05 Mar 2019 06:10 |
| URI: | http://repository.its.ac.id/id/eprint/47845 |
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