Some iteration procedures and weighted mean matrix

In this study which consist of six chapters, some results relating to convergence of Mann iteration procedure to the fixed point of some transformation classes have been obtained by the help of weighted mean matrix which is generalization of Cesàro, Riezs and Nörlund means. In the first chapter, literature summary is given about historical process of the fixed point theory and summability. In the second chapter, the basic definitions and theorems which are used in the process of this study have been given. In the third chapter, some iteration procedures which reach up to today as a wide field of study have been compiled. In the fourth chapter, using reguler type weighted mean matrix, it has been proven that Mann iteration converges to fixed point of continous transformations. In the five chapter, defining Mann iteration of weigted mean, strong and weak convergence of asymptotically nonexpansive transformation classes have been examined. In the last chapter of the thesis, the results obtained from our study have been given.