İki değişkenli q-Bleimann, Butzer ve Hahn operatörlerinin yaklaşım özellikleri
Özet
Bu tez dort bolumden olusmaktadr. Ilk bolum giris ksmna ayrlmstr.Ikinci bolumde baz temel kavramlardan bahsedilmistir. Srasyla lineer pozitifoperator dizileri, sureklilik modulu, Lipschitz snf fonksiyonlar, operatordizilerinin duzgun yaknsaklg, Bleimann, Butzer ve Hahn operatorleri, q-analizkavramlar tantlp bunlara iliskin bilinen baz sonuclar hatrlatlmstr.Ucuncu bolumde, q-Bleimann, Butzer ve Hahn operatorlerinin iki degiskenli halitanmlanmstr. Bu operatorlerin, reel uzayn snrl ve surekli bir alt uzaynda,surekli bir fonksiyona duzgun yaknsadg gosterilmistir. Ayn zamanda operatorlerin yaklasm hz, sureklilik modulu ve Lipschitz tipli maksimal fonksiyonlaryardmyla degerlendirilmistir.Son bolumde ise istatistiksel yaknsaklk kavram hatrlatlms ve daha sonratek ve iki degiskenli q-Bleimann, Butzer ve Hahn operatorlerinin istatistikselyaklasm ozellikleri elde edilmistir. Ayrca bu operatorlere iliskin yaklasmnhz istatistiksel olarak yorumlanmstr.Abstract This thesis consists of four chapters. The first chapter has been devoted to theintroduction.In the second chapter, some basic concepts have been mentioned. The conceptsof the sequences of linear positive operator, modulus of continuity, Lipschitztype maximal functions, uniform convergence of the sequences of the operators,Bleimann, Butzer and Hahn operators, q-analysis have been recalled respectivelyand some known results concerning these concepts have also been considered.In the third chapter, q-Bleimann, Butzer and Hahn operators with two variableshave been introduced. The uniform convergence of these operators to the continuousfunction dened on a bounded and continuous subset of real numbershas been proved. Furthermore the order of approximation of these operatorshas also been considered with the help of modulus of continuity and Lipschitztype maximal functions.In the last chapter, the concept of the statistical convergence has been recalledand then the statistical convergence properties of the q-Bleimann, Butzer andHahn operators with one and two variables have been obtained. Also the orderof approximation concerning the operators has been interpreted statistically.