Some linear positive operators in weighted spaces

The thesis consist of four chapters. The first chapter has been devoted to the introduction. In the second chapter, general informations about the linear positive operators and q- analysis are given. In the third chapter, a generalization of the Meyer-König ve Zeller operators based on q-integers are introduced and some convergence properties of these operators are investigated in weighted spaces of continous functions with the help of weighted Korovkin-type theorem. In addition, the rates of approximation of these operators are obtained with the help of the modulus of continuity and the weighted modulus of continuity. Moreover an application to differential equation related to q- derivatives and later a Stancu-type remainder are given. In the fourth chapter, a generalization of the Szasz-Mirakjan operators based on q- integers are introduced and some convergence properties of these operators are given. Therefore, the rates of approximation of these operators are obtained by means of modulus of continuity and the weighted modulus of continuity. Voronovskaja-type formula for these operators is discussed.