In this paper, an iterative algorithm is introduced to solve the split common fixed point problem for asymptotically nonexpansive mappings in Hilbert spaces. The iterative algorithm presented in this paper is shown to possess strong convergence for the split common fixed point problem of asymptotically nonexpansive mappings although the mappings do not have semi-compactness. Our results improve and develop previous methods for solving the split common fixed point problem.

In this paper, we investigate a splitting algorithm for treating monotone operators. Strong convergence theorems are established in the framework of Hilbert spaces.

In this paper, a regularization method for treating zero points of the sum of two monotone operators is investigated. Strong convergence theorems are established in the framework of Hilbert spaces.

In this paper, a new iterative method for finding the projection onto the intersection of two closed convex sets in the framework of Banach spaces is presented. It is a viscosity approximation method which produces a strongly convergent sequence.

In this paper, we introduce a new algorithm for solving split equality mixed equilibrium problems in the framework of infinite-dimensional real Hilbert spaces. The strong and weak convergence theorems are obtained. As application, we shall utilize our results to study the split equality mixed variational inequality problem and the split equality convex minimization problem. Our results presented in this paper improve and extend some recent corresponding results.

A number of practical problems in science and engineering can be converted into a system of nonlinear equations and therefore, it is imperative to develop efficient methods for solving such equations. Due to their nice convergence properties and low storage requirements, conjugate gradient methods are considered among the most efficient for solving large-scale nonlinear equations. In this paper, a modified conjugate gradient method is proposed based on a projection technique and a suitable line search strategy. The proposed method is matrix-free and its sequence of search directions satisfies sufficient descent condition. Under the assumption that the underlying function is monotone and Lipschitzian continuous, the global convergence of the proposed method is established. The method is applied to solve some benchmark monotone nonlinear equations and also extended to solve ${\ell }_1$ -norm regularized problems to reconstruct a sparse signal in compressive sensing. Numerical comparison with some existing methods shows that the proposed method is competitive, efficient and promising.