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In this paper, a Halpern–Tseng-type algorithm for approximating zeros of the sum of two monotone operators whose zeros are J-fixed points of relatively J-nonexpansive mappings is introduced and studied. A strong convergence theorem is established in Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorem to convex minimization and image-restoration problems are presented. In addition, the proposed algorithm is used in solving some classical image-recovery problems and a numerical example in a Banach space is presented to support the main theorem. Finally, the performance of the proposed algorithm is compared with that of some existing algorithms in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish the stability and strong convergence theorems, for the three-step iteration with perturbations for a T-Ciric quasicontraction, in the environment of the CAT(0) space. Finally, an application to the integral-type contraction and an example are shown. [ABSTRACT FROM AUTHOR]

In this paper, relaxed and relaxed inertial modified Tseng algorithms for approximating zeros of sum of two monotone operators whose zeros are fixed points or J-fixed points of some nonexpansive-type mappings are introduced and studied. Strong convergence theorems are proved in the setting of real Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorems to the concept of J-fixed point, convex minimization, image restoration and signal recovery problems are also presented. In addition, some interesting numerical implementations of our proposed methods in solving image recovery and compressed sensing problems are presented. Finally, the performance of our proposed methods are compared with that of some existing methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new accelerated iterative method for finding a common fixed point of a countable family of nonexpansive mappings in the Hilbert spaces framework. Using our main result, we obtain a new accelerated image restoration iterative method for solving a minimization problem in the form of the sum of two proper lower semi-continuous and convex functions. As applications, we apply our algorithm to solving image restoration problems. [ABSTRACT FROM AUTHOR]

Restoring images corrupted by Poisson noise have attracted much attention in recent years due to its significant applications in image processing. There are various regularization methods of solving this problem and one of the most famous is the total variation (TV) model. In this paper, we present a new method based on accelerated alternating minimization algorithm (AAMA) which involves minimizing the sum of a Kullback–Leibler divergence term and a TV term for restoring Poisson noise degraded images. Our proposed algorithm is applied in solving the aforementioned problem and its convergence analysis is established under very weak conditions. In addition, the numerical examples reported demonstrate the efficiency and versatility of our method compared to existing methods of restoring images with Poisson noise. [ABSTRACT FROM AUTHOR]

We introduce a modified inertial double Mann type iterative method to approximate coupled solutions of a bivariate nonexpansive operator T : C × C → C, where C is a nonempty closed and convex subset of a Hilbert space. The one theorem and complement important old and recent results in coupled fixed point theory. Some appropriate examples to illustrate our results and their generalization are also given. [ABSTRACT FROM AUTHOR]

In this paper, we modify the proximal point algorithm for finding common fixed points in CAT(0) spaces for nonlinear multivalued mappings and a minimizer of a convex function and prove Δ‐convergence of the proposed algorithm. A numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the split common fixed point problem in Hilbert spaces. We find a common solution of the split common fixed point problem for two demicontractive operators without a priori knowledge of operator norms. A strong convergence theorem is obtained under some additional conditions and numerical examples are included to illustrate the applications in signal compressed sensing and image restoration. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a new viscosity iterative method minimization algorithm for image restoration algorithm is proposed. Based on a new viscosity iteration, the algorithm for finding the common zeros of two accretive operators in the framework of uniformly smooth Banach spaces. Moreover, the strong convergence theorems for the iterative algorithms and an example is proposed which shows the validity of main theorem are proved. The results of this paper are improved and extended of the corresponding ones announced by many others and we also applied our result to solve a convex minimization problem and Gâteaux differentiable E P s and Variational Inequality. Experiment results show that the proposed algorithms outperform some other methods. Finally, we give the numerical experiments to show the efficiency and advantage of the proposed methods and we also used our proposed algorithm for applying to solve the image deblurring and image recovery problems. [ABSTRACT FROM AUTHOR]