Urysohn-tipi lineer olmayan integral operatörler ailesinin noktasal yakınsaklığı
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Dosyalar
Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Kırıkkale Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tez beş bölümden oluşmaktadır. İlk bölüm, tezin girişine ayrılmış olup bu bölümde, Yaklaşımlar Teoerisi'nin başlangıcından günümüze kadar olan gelişim sürecine genel bir bakışta bulunulmuş; bu teorinin belli başlı çalışmalarına değinilmiş ve tezimizin asıl konusu olan lineer olmayan integral operatörlerle yaklaşımdan bahsedilmiştir. Bu tezin amacına ve çalışmada referans alınan kaynaklara ilişkin özete yine birinci bölümde yer verilmiştir. İkinci bölümde, çalışmada ihtiyaç duyulacak temel tanım, teoerem ve lemmalar verilmiş ve Urysohn-tipi lineer olmayan integral operatörler ailesi ve çekirdeği tanıtılmıştır. Üçüncü bölümde, Sevgi ESEN ALMALI'nın "On pointwise convergence of the family of Urysohn-type integral operators" isimli çalışmasındaki yakınsaklık problemleri detaylı bir şekilde ele alınmış ve devamında Urysohn-tipi lineer olmayan integral operatörler ailesinin L_p-uzayındaki yakınsaklığı ile ilgili bazı orijinal sonuçlar verilmiştir. Dördüncü bölümde, tezde elde edilen bulgular tartışılmış, beşinci bölüm ise sonuç ve önerilere ayrılmıştır.
This thesis consists of five chapters. The first chapter is devoted to the introduction of the thesis, and in this chapter, an overview of the development process of the Theory of Approximation from the beginning to the present is given; the basic studies of this theory are mentioned and some explanations are made about the approximation with nonlinear integral operators, which is the main subject of our thesis. The purpose of this thesis and the summary of the sources in the study are also included in the first chapter. In the second chapter, the basic definitions, theorems and lemmas that will be needed in the study are given and the family and kernel of Urysohn-type nonlinear integral operators are introduced. In the third chapter, convergence problems in Sevgi ESEN ALMALI's study titled "On pointwise convergence of the family of Urysohn-type integral operators" are examined in detail and then some original results are given about the convergence of the family of Urysohn-type nonlinear integral operators in L_p. While the findings obtained in the thesis are discussed in the fourth section, the fifth section is devoted to conclusions and recommendations.
This thesis consists of five chapters. The first chapter is devoted to the introduction of the thesis, and in this chapter, an overview of the development process of the Theory of Approximation from the beginning to the present is given; the basic studies of this theory are mentioned and some explanations are made about the approximation with nonlinear integral operators, which is the main subject of our thesis. The purpose of this thesis and the summary of the sources in the study are also included in the first chapter. In the second chapter, the basic definitions, theorems and lemmas that will be needed in the study are given and the family and kernel of Urysohn-type nonlinear integral operators are introduced. In the third chapter, convergence problems in Sevgi ESEN ALMALI's study titled "On pointwise convergence of the family of Urysohn-type integral operators" are examined in detail and then some original results are given about the convergence of the family of Urysohn-type nonlinear integral operators in L_p. While the findings obtained in the thesis are discussed in the fourth section, the fifth section is devoted to conclusions and recommendations.
Açıklama
Anahtar Kelimeler
Matematik, Mathematics
