Fixed point iterations for nonexpansive maps and their applications to constrained minimization and feasibility problems in Hilbert spaces

The purpose of this study is to prove a faster iterative scheme than all of Thakur et al., Abbas and Nazir, Noor, Agarwal et al., Ishikawa, Picard-Mann, Mann and Picard iterations in the literature. The paper introduced three novel modified multistep iterative schemes (A), (B) and (C). Fixed point theorems are proven with these newly introduced multistep iterative schemes for the class of contraction mappings with fixed point p=Tp and nonexpansive mappings respectively. The rate of convergence was demonstrated numerically with the help of Python program and the results showed that our modified iterative scheme (C) converge in lesser number of iterations than existing iterative schemes in the literature. With the help of well constructed theorems, these modified multistep iterative schemes were applied to constrained minimization and split feasibility problems for the class of nonexpansive mappings in real Hilbert spaces.