Nisa’, Hilwin (2015) Kestabilan persamaan fungsional Jensen. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.
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Abstract
INDONESIA:
Persamaan fungsional Jensen merupakan salah satu variasi dari persamaan fungsional Cauchy additive. Suatu persamaan fungsional dapat diaplikasikan sebagai model dari suatu proses fisik ketika persamaan fungsional tersebut stabil. Sehingga dengan diketahuinya kestabilan dari persamaan fungsional Jensen, dapat dijadikan landasan para peneliti yang akan mengaplikasikan persamaan fungsional Jensen. Adapun konsep kestabilan yang digunakan dalam penelitian ini adalah konsep kestabilan Hyers-Ulam-Rassiass. Jika persamaan fungsional Jensen terbukti memenuhi teorema Hyers-Ulam-Rassias, maka dapat dikatakan bahwa persamaan fungsional Jensen tersebut stabil.
Pada skripsi ini ditunjukkan bahwa persamaan fungsional Jensen terbukti memenuhi teorema Hyers-Ulam-Rassias. Untuk mengilustrasikan kestabilan persamaan fungsional Jensen, pada skripsi ini diberikan contoh persamaan Jensen dan kemudian digambarkan grafiknya. Karena persamaan fungsional Jensen terbukti memenuhi teorema Hyers-Ulam-Rassias, maka dapat dikatakan bahwa persamaan fungsional Jensen tersebut stabil.
ENGLISH:
Jensen functional equation is one of variation of additive Cauchy functional equation. Jensen functional equation can be applied as a model of a physical process when it is stable. Therefore, by knowing the stability of Jensen functional equation, it give the other researchers reference to apply Jensen functional equation. The concept of stability that is used in this research is Hyers-Ulam-Rassiass stability. If Jensen functional equation satisfy Hyers-Ulam-Rassiass theorem, it can be said that Jensen functional equation is stable.
This thesis showed that Jensen functional equation has been proven to satisfy Hyers-Ulam-Rassias theorem. To illustrate the stability of Jensen functional equation, in this thesis the example of Jensen equation is given and then the graph is illustrated. Since the functional equation Jensen has proven to satisfy Hyers-Ulam-Rassias theorem, it can be said that Jensen functional equation is stable.
| Item Type: | Thesis (Undergraduate) | |||||||||
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| Supervisor: | Rahman, Hairur and Sujarwo, Imam | |||||||||
| Contributors: |
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| Keywords: | Persamaan Fungsional Cauchy Additive; Persamaan Fungsional Jensen; Kestabilan Hyers-Ulam-Rassias; Additive Cauchy Functional Equation; Jensen Functional Equation; Hyers-Ulam-Rassias Stability | |||||||||
| Subjects: | 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010101 Algebra and Number Theory 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010108 Operator Algebras and Functional Analysis 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010111 Real and Complex Functions (incl. Several Variables) 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010112 Topology |
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| Departement: | Fakultas Sains dan Teknologi > Jurusan Matematika | |||||||||
| Depositing User: | Ahmad Zaini | |||||||||
| Date Deposited: | 16 May 2017 15:21 | |||||||||
| Last Modified: | 16 May 2017 15:21 | |||||||||
| URI: | http://etheses.uin-malang.ac.id/id/eprint/6529 |
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