Admissible perturbations of alpha-psi-pseudocontractive operators: convergence theorems

In the last decades, the study of convergence of fixed point iterative methods has received an increasing attention, due to their performance as tools for solving numerical problems. As a consequence of this fact, one can access to a wide literature on iterative schemes involving different types of operators; see [2, 4, 5]. We point out that fixed point iterative approximation methods have been largely applied in dealing with stability and convergence problems; see [1, 6]. In particular, we refer to various control and optimization questions arising in pure and applied sciences involving dynamical systems, where the problem in study can be easily arranged as a fixed point problem. Then, we prove some convergence theorems for a certain class of operators in real Hilbert spaces. Precisely, by using the concept of admissible perturbation of alpha-psi-pseudocontractive operators in Hilbert spaces, we establish results for Krasnoselskij type fixed point iterative schemes. Our theorems complement, generalize and unify some existing results; see [3, 4]