Approximation by gauss weierstrass integral operator

In this thesis, the approximation of the general Weierstrass singular integral in Orlicz spaces is investigated. The thesis consists of five chapters. The first chapter defines the method and purpose of the study. In The second chapter presents fundamental definitions and theorems, such as normed space, Lebesgue space, convolution, integral operator, dense subset, Fejer type singular integral, and quasi-convex functions. In the third chapter, Orlicz spaces, which are the generalization of Lebesgue space, are discussed and the Young function and its conjugate Young function in these spaces are examined. Using these functions, Orlicz spaces are defined and information about dual spaces and some dense subsets under certain conditions is given. In the fourth chapter defines the Gauss-Weierstrass singular integral, a Fejer type singular integral, and explains the some definitions and theorems related to the general GaussWeierstrass singular integral. In the final chapter, the approximation of the general Weierstrass singular integral in Orlicz spaces is addressed, and the proof of this approximation is presented.