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In this article, we introduce and study some strong convergence theorems for a mixed-type SP-iteration for three asymptotically nonexpansive self-mappings and three asymptotically nonexpansive nonself-mappings in uniformly convex hyperbolic spaces. In addition to that, we provide an illustrative example. The findings here expand and improve upon some of the relevant conclusions found in the published literature.

In this article, weak and strong convergence theorems of the M-iteration method for 𝒢-nonexpansive mapping in a uniformly convex Banach space with a directed graph were established. Moreover, weak convergence theorem without making use of Opial’s condition is proved. The rate of convergence between the M-iteration and some other iteration processes in the literature was also compared. Specifically, our main result shows that the M-iteration converges faster than the Noor and SP iterations. Finally, the numerical examples to compare convergence behavior of the M-iteration with the three-step Noor iteration and the SP-iteration were given. As application, some numerical experiments in real-world problems were provided, focused on image deblurring and signal recovering problems.

This work proposes a novel Noor iterative scheme, called CT‐iteration, to approximate the fixed points in the new context of generalized nonexpansive mappings with property (E)$$ (E) $$. We establish the strong and weak convergence results in a uniformly convex Banach space. Additionally, numerical examples of the iterative technique are demonstrated using a signal recovery application in a compressed sensing situation. Furthermore, we show the use of the proposed method to generate polynomiographs. The proposed algorithm has been implemented and tested via numerical simulation in MATLAB. The simulation results show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

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 discussed. As applications, we apply PISPMHA to solve linear system, differential, and signal recovery problems. [ABSTRACT FROM AUTHOR]

In this paper, using sunny nonexpansive retractions, which are different from the metric projection in Banach spaces, a new type of study regarding the iterative methods in view of two quasi‐nonexpansive nonself mappings is presented. We also give the convergence analysis for the proposed method in the background of uniformly convex Banach spaces. Moreover, we apply our results to find solutions of common zeros of accretive operators, convexly constrained least square problems, and convex minimization problems. Furthermore, we also discuss novel applications of these methods to differential problems, image deblurring, and signal recovering problems. [ABSTRACT FROM AUTHOR]