Bazı özel fonksiyonlar ile analitik fonksiyonların yaklaşımı
Küçük Resim Yok
Tarih
2013
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
İstanbul Ticaret Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Beş bölümden oluşan bu çalışmada bazı diferansiyel denklemlerin Hyers-Ulam kararlılığı incelenmiştir.Bu çalışmanın birinci ve ikinci bölümünde konuya giriş yapılmış ve literatüre değinilmiştir. Üçüncü bölümde ise daha sonra kullanılacak olan temel tanım ve teoremlere yer verilmiştir. Dördüncü bölümde, birinci mertebeden lineer homojen ve homojen olmayan diferansiyel denklemlerin Hyers-Ulam kararlılığı incelenerek üstel fonksiyonların yaklaşım özelliği ele alınmıştır. Bu çalışmanın beşinci bölümünde ise Airy, Legendre, Hermite ve Chebyshev diferansiyel denklemlerinin çözümleri bulunmuş olup buradan elde edilen sonuçlar her analitik fonksiyonun bu özel fonksiyonlar tarafından belli bir hata sınırı ile yaklaştırılabileceğinin ispatlanmasında kullanılmıştır. Anahtar Kelimeler: Diferansiyel Denklemlerin Kararlılığı, Hyers-Ulam Kararlılık, Airy denklemi, Legendre denklemi, Hermite denklemi, Chebyshev denklemi
In this study consisting of five sections, Hyers-Ulam stability of some differential equations were investigated. In the first and second sections of the study, introduction to the subject in hand and the relevant literature were mentioned. In the third section, the basic definitions and theorems which will be utilized were stated. In the fourth section, Hyers-Ulam stability of first order linear homogeneous and nonhomogeneous differential equations and approximation property of exponential functions were examined. In fifth section of this study inhomogeneous Airy, Legendre, Hermite and Chebyshev differential equations were solved and these results applied to prove every analytic functions can be approximated by these special functions with an error bound. Key words: Hyers-Ulam stability, The stability of differential equations, Airy equation, Legendre equation, Hermite equation, Chebyshev equation
In this study consisting of five sections, Hyers-Ulam stability of some differential equations were investigated. In the first and second sections of the study, introduction to the subject in hand and the relevant literature were mentioned. In the third section, the basic definitions and theorems which will be utilized were stated. In the fourth section, Hyers-Ulam stability of first order linear homogeneous and nonhomogeneous differential equations and approximation property of exponential functions were examined. In fifth section of this study inhomogeneous Airy, Legendre, Hermite and Chebyshev differential equations were solved and these results applied to prove every analytic functions can be approximated by these special functions with an error bound. Key words: Hyers-Ulam stability, The stability of differential equations, Airy equation, Legendre equation, Hermite equation, Chebyshev equation
Açıklama
Fen Bilimleri Enstitüsü, Matematik Ana Bilim Dalı
Anahtar Kelimeler
Matematik, Mathematics
