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In this paper, we present a modified SP iteration with the inertial technical term for three quasi-nonexpansive multivalued mappings in a Hilbert space. We then obtain weak convergence theorem under suitable conditions. The strong convergence theorems are given using CQ and shrinking projection methods with our modified iteration. Finally, we test some numerical experiments to illustrate that our inertial forward–backward method with the inertial technique term has a more effective convergence than that of the standard forward–backward method and Halpern algorithm.

In the present article, an efficient modified three-step iteration algorithm for solving a common fixed point of three G-nonexpansive mappings is constructed. Weak and strong convergence theorems are established by assuming coordinate-convexity for the proposed scheme in a uniformly convex Banach space endowed with a directed graph under some suitable control conditions. Moreover, we then establish weak convergence theorem without making use of the Opial’s condition. We also provide some numerical examples for confirming our main theorem and compare convergence behavior of our algorithm with the three-step Noor iteration and the SP-iteration. We found that our algorithm has faster than Noor and SP iterations. As applications, we use our proposed algorithm to solve image deblurring problems. Furthermore, we present the new idea in solving signal recovery in situations without knowing the type of noises.

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.

The split feasibility problem (SFP) in Hilbert spaces is addressed in this study using an efficient iterative approach. Under mild conditions, we prove convergence theorems for the algorithm for finding a solution to the SFP. We also present numerical examples to illustrate that the acceleration of our algorithm is effective. Our results are applied to solve image deblurring and signal recovery problems. Furthermore, we show the use of the proposed method to generate polynomiographs.

In this paper, we propose inertial forward-backward splitting algorithm to approximate the solution of common variational inclusion problems. By using the inertial technique with parallel monotone hybrid methods we prove strong convergence results under some suitable conditions in Hilbert spaces. We then give some applications and numerical experiments for supporting our main results which shows that our proposed inertial hybrid method has better convergence rate than existing algorithms. Further, we apply our result to solve a common convex minimization problem and a common split feasibility problem. Finally, we use our proposed algorithm to solve the unconstrained image restoration problems and we can show that our algorithm is flexibility and good quality to use for common types of blur effects.

In this work, we modify the inertial type parallel monotone hybrid algorithm with Armijo linesearch to solve common nonmonotone equilibrium problems. The weak convergence theorem is established under some suitable conditions in Hilbert spaces. Finally, the numerical example is shown to support our main result. The efficiencies of the proposed algorithm are presented by comparing with previously parallel algorithms in novel image restoration. It's illustrated that the proposed algorithm can increase deblurring quality when the subproblems are increasing. [ABSTRACT FROM AUTHOR]