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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]

The purpose of this paper was to prove that a novel algorithm with an inertial approach, used to generate an iterative sequence, strongly converges to a fixed point of a nonexpansive mapping in a real uniformly convex Banach space with a uniformly Gâteaux differentiable norm. Furthermore, zeros of accretive mappings were obtained. The proposed algorithm has been implemented and tested via numerical simulation in MATLAB. The simulation results showed that the algorithm converges to the optimal configurations and shows the effectiveness of the proposed algorithm. [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]

In this work, we aim to prove the strong convergence of the sequence generated by the modified inertial parallel viscosity-type algorithm for finding a common fixed point of a finite family of nonexpansive mappings under mild conditions in real Hilbert spaces. Moreover, we present the numerical experiments to solve linear systems and differential problems using Gauss–Seidel, weight Jacobi, and successive over relaxation methods. Furthermore, we provide our algorithm to show the efficiency and implementation of the LASSO problems in signal recovery. The novelty of our algorithm is that we show that the algorithm is efficient compared with the existing algorithms. [ABSTRACT FROM AUTHOR]

For finding a common fixed point of a finite family of G-nonexpansive mappings, we implement a new parallel algorithm based on the Ishikawa iteration process with the inertial technique. We obtain the weak convergence theorem of this algorithm in Hilbert spaces endowed with a directed graph by assuming certain control conditions. Furthermore, numerical experiments on the diffusion problem demonstrate that the proposed approach outperforms well-known approaches. [ABSTRACT FROM AUTHOR]

In this work, we modify the inertial hybrid algorithm with Armijo line search using a parallel method to approximate a common solution of nonmonotone equilibrium problems in Hilbert spaces. A weak convergence theorem is proved under some continuity and convexity assumptions on the bifunction and the nonemptiness of the common solution set of Minty equilibrium problems. Furthermore, we demonstrate the quality of our inertial parallel hybrid algorithm by using image restoration, as well as its superior efficiency when compared with previously considered parallel algorithms. [ABSTRACT FROM AUTHOR]

In the present article, we establish weak and strong convergence theorems of a new modified three-step iteration method for three G-nonexpansive mappings in a uniformly convex Banach space with a directed graph. Moreover, weak convergence theorem without making use of the Opial's condition is proved. We also show the numerical experiment for supporting our main results and comparing rate of convergence of the new modified three-step iteration with the three-step Noor iteration and the SP iteration. We also provide some numerical examples to illustrate the convergence behavior and advantages of the proposed method. Furthermore, we apply our results to find solutions of constrained minimization problems and split feasibility problems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general iterative scheme based on CQ projection method for finding a common solution of system of equilibrium problems and the fixed point set of a finite family of demicontractive mappings. We also prove strong convergence of the scheme to a common element of the two above‐described sets. We then give a numerical example to justify our main result. An example is given in an infinite dimensional space for supporting our main result. Moreover, we apply our main result to solve the unconstrained image restoration problems with a finite family of blurring operators. Our results extend and improve some existing results in the literature. [ABSTRACT FROM AUTHOR]