Quasilineer uzaylar arasında tanımlı quasilineer operatörler üzerine
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Dosyalar
Tarih
2014
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Yayıncı
İnönü Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu çalışmada genel olarak, quasilineer operatörler teorisinin geliştirilmesi amaçlanmış ve lineer operatörlere ilişkin bazı önemli teoremlerin quasilineer karşılıkları verilmiştir. Beş bölümden oluşan bu çalışmanın ilk bölümünde küme-değerli fonksiyon sınıflarının bazı özelliklerinden bahsedilmiş ve bu sınıflara ait önemli örnekler verilmiştir. Ikinci bölüm ise sonraki bölümlere temel teşkil edecek bazı önemli tanım ve teoremlerin verilmesine ayrılmıştır. Ayrıca R^n nin kompakt ve kompakt-konveks alt kümelerinin ailesinden bahsedilmiştir. Üçüncü bölümde quasilineer uzay ve altquasilineer uzay kavramı ele alınmış, normlu quasilineer uzaylardan bahsedilmiştir. Dördüncü bölümde quasilineer bağımlılık-bağımsızlık tanımları verilmiş, baz ve boyut kavramları tanıtılmıştır. Ayrıca proper quasilineer uzaylardan bahsedilmiştir. Beşinci ve son bölümde ise quasilineer operatörler ve bu operatörlerle ilgili yeni sonuçlar sunulmuştur. Ayrıca hem reel hem de interval matrisler yardımıyla elde quasilineer operatörler verilmiştir.
In this work, which consists of five chapter, our main object is to develop the theory of quasilinear operations and quasilinear counterparts of some important theorems and corollaries with respect to linear operations have been stated. In the first chapter, some properties related to families of set-valued function have been presented and important examples have been given for this families. In the second chapter, the basic definitions and theorems which will be useful in the next chapters have been introduced. Also, the family of compact and convex subsets of Rn has been mentioned. In the third chapter, after the introduction of quasilinear spaces and quasilinear subspaces, normed quasilinear spaces have been considered. In the fourth chapter, the concept of quasilinear depandence-independence have been introduced, the notions of bases and dimension have been stated. Furthermore, proper quasilinear spaces have been introduced. In the fifth and final chapter, quasilinear operators and new corollaries with respect to these operations have been presented. In addition, quasilinear operations optained by the way of both real matrix and interval matrix have been discussed.
In this work, which consists of five chapter, our main object is to develop the theory of quasilinear operations and quasilinear counterparts of some important theorems and corollaries with respect to linear operations have been stated. In the first chapter, some properties related to families of set-valued function have been presented and important examples have been given for this families. In the second chapter, the basic definitions and theorems which will be useful in the next chapters have been introduced. Also, the family of compact and convex subsets of Rn has been mentioned. In the third chapter, after the introduction of quasilinear spaces and quasilinear subspaces, normed quasilinear spaces have been considered. In the fourth chapter, the concept of quasilinear depandence-independence have been introduced, the notions of bases and dimension have been stated. Furthermore, proper quasilinear spaces have been introduced. In the fifth and final chapter, quasilinear operators and new corollaries with respect to these operations have been presented. In addition, quasilinear operations optained by the way of both real matrix and interval matrix have been discussed.
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Banazılı, H. K. (2014). Quasilineer uzaylar arasında tanımlı quasilineer operatörler üzerine. İnönü Üniversitesi Fen Bilimleri Enstitüsü. 1-98 ss.
