The aim of this paper is to propose a novel Noor iteration technique, called the CT-iteration for approximating a fixed point of continuous functions on closed interval. Then, a necessary and sufficient condition for the convergence of the CT-iteration of continuous functions on closed interval is established. We also compare the rate of convergence between the proposed iteration and some other iteration processes in the literature. Specifically, our main result shows that CT-iteration converges faster than CP-iteration to the fixed point. We finally give numerical examples to compare the result with Mann, Ishikawa, Noor, SP and CP iterations. Our findings improve corresponding results in the contemporary literature.

For solving a common fixed point of a finite family of G-nonexpansive mappings, we propose a parallel inertial SP-iteration monotone hybrid algorithm (PISPMHA). Weak convergence theorem is established for PISPMHA in Hilbert spaces endowed with graphs. Convergence behavior of PISPMHA is analyzed and dis- cussed. As applications, we apply PISPMHA to solve linear system, differential, and signal recovery problems.