Approximation properties of classes of some Gadjiev-İbragimov type operators

The first chapter in this thesis is devoted to fundamental definitions and theorems. In this chapter general properties of some function spaces are presented. General properties of linear positive operators are given, and Korovkin Type approximation theorems in spaces C[a,b], C_ρ (R), 〖 C〗_ρ^k (R) are investigated. General properties of classical modulus of continuity for spaces C[a,b] and 〖 C〗_ρ^k (R) are given. In the second chapter, in C[0,A] space classic Gadjiev-İbragimov operators and two different generalizations of the Gadjiev-Ibragimov operators are defined .The rate of convergence of classic Gadjiev-İbragimov operators and these generalizations of the Gadjiev-Ibragimov operators are investigated by means of the usual definition modulus of continuity. In the third chapter ,by defining some generalizations of the Gadjiev-Ibragimov operators in unbounded sets,their approximation properties are given. Approximation speeds of these operators are studied by the weighted modulus of continuity. In the last chapter, results and suggestions are given.