An approximation for sequences of linear positive operators in weighted spaces

The first chapter in this thesis is devoted to fundamental definitions and theorems In this chapter general properties of some function spaces are presented.In the second chapter general properties of linear positive operators are given, and approximation theorems for Korovkin Type in spaces C[a,b], C_? (R^m ) and B_? (R^m ) are introduced.In the third chapter, general properties of classical modulus of continuity for spaces C[a,b] and C_? [0,?? ) ? are given.In the fourth chapter; by defining space C_2m, in the subspace C_2m^0 of C_2m the existence of the theorem for Korovkin type is proved. However, it is established that in space C_2m an analogous theorem is invalid. By defining modulus of continuity in weighted space C_2m^0, approximation to the functions in the space C_2m^0 is examined via Gadjiev-Ibragimov operatorswhich are known in literature. An equality for n.th moment of Gadjiev-Ibragimov operator is proved and approximation speed is studied by the modulus of continuity.