Bayram, ElgizEsen, Sevgi2022-04-082022-04-082002http://hdl.handle.net/20.500.12575/78574This thesis consist of five chapters. First chapter is devoted to the intro duction. In the second chapter, definitions that are necessary for this work, approximation theory, characteristic points are examined. Moreover, some theorems about convergence and the order of convergence at these points are given. In the third chapter, a brand new inequality about continuity module of nonconvolution type integral operators and a simple property of these operators are given. In the fourth chapter, it is investigated that at the Lebesque and continuity points, pointwise convergence and order of con vergence of nonconvolution type integral operators family to non integrable functions using a different method. In the fifth chapter, at the p-Lebesque point, convergence and order of convergence of these type integral operators family to the functions that are not in Lp- space is given. 2002, 87 pages Key Words : In Operators Family, Convergence and The Order of Convergence, Nonconvolution Type Integral Operators, Lebesque Point.trMetematikdoctoralThesis