Kestabilan persamaan fungsional Jensen-Hosszú

Nadhifa, Zukhrufun (2016) Kestabilan persamaan fungsional Jensen-Hosszú. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.

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Abstract

INDONESIA:

Persamaan fungsional Jensen-Hosszú adalah persamaan fungsional yang dikonstruksikan dari persamaan fungsional Jensen dan Hosszú yang merupakan variasi dari persamaan fungsional Cauchy additive. Suatu persamaan fungsional dapat diaplikasikan sebagai model dari suatu proses fisik apabila persamaan fungsional tersebut dinyatakan stabil. Konsep kestabilan yang digunakan dalam skripsi ini mengikuti konsep kestabilan Hyers-Ulam dan Hyers-Ulam-Rassias.

Hasil dari skripsi ini adalah persamaan fungsional Jensen-Hosszú dikatakan stabil dengan menggunakan konsep kestabilan Hyers-Ulam dengan indikator:
a. .... adalah barisan Cauchy .....
b. Jika ..... maka A adalah fungsi additive.
c. A memenuhi ......
d. A adalah fungsi yang tunggal.
Begitu pun dengan menggunakan konsep kestabilan Hyers-Ulam-Rassias persamaan fungsional Jensen-Hosszú dikatakan stabil dengan indikator:
a. .... adalah barisan Cauchy .....
b. Jika ..... maka A adalah fungsi additive.
c. A memenuhi ......
d. A adalah fungsi yang tunggal.

Salah satu contoh fungsi yang memenuhi persamaan fungsional Jensen-Hosszú adalah .... Terbukti pula bahwa contoh fungsi tersebut stabil berdasarkan konsep kestabilan Hyers-Ulam dan Hyers-Ulam-Rassias.

ENGLISH:

Jensen-Hosszú functional equation is constructed from Jensen and Hosszú functional equation that are the variations of Cauchy additive functional equation. A functional equation can be applied as a model of physic progress if it is stable. Stability concept that used in this thesis is Hyers-Ulam and Hyers-Ulam-Rassias’ concept.

The result of this thesis is that Jensen-Hosszú functional equation is stable based on Hyers-Ulam’s stability concept based on the following indicators:
a. .... is a Cauchy sequence .....
b. If ..... then A is additive function.
c. A satisfies ......
d. A is unique.
As well as by using Hyers-Ulam-Rassias’ stability concept, Jensen-Hosszú functional equation is said stable based on the following indicators:
a. .... is a Cauchy sequence ....
b. If ...... then A is additive function.
c. A satisfies .....
e. A is unique.

One example of a function that satisfies Jensen-Hosszú functional equation is ..... It is proven also that the function is stable according to Hyers-Ulam and Hyers-Ulam-Rassias’ stability concept.

Item Type: Thesis (Undergraduate)
Supervisor: Rahman, Hairur and Rozi, Fachrur
Keywords: Persamaan fungsional Cauchy additive; Persamaan fungsional Jensen-Hosszú; Konsep kestabilan Hyers-Ulam-Rassias; Cauchy additive functional equation; Jensen-Hosszú functional equation; Hyers-Ulam-Rassias concept of stability
Departement: Fakultas Sains dan Teknologi > Jurusan Matematika
Depositing User: Nugroho Dwi Setyanto
Date Deposited: 27 Jul 2016 08:59
Last Modified: 27 Jul 2016 08:59
URI: http://etheses.uin-malang.ac.id/id/eprint/3850

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