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This paper addresses the problem of seeking a common fixed point for a collection of nonexpansive operators over time-varying multi-agent networks in real Hilbert spaces, where each operator is only privately and approximately known to each…
We introduce and analyze an abstract algorithm that aims to find the projection onto a closed convex subset of a Hilbert space. When specialized to the fixed point set of a quasi nonexpansive mapping, the required sufficient condition…
This paper is devoted to the problem of finding a common fixed point of quasinonexpansive mappings defined on a Hilbert space. To approximate the solution to this problem, we present several iterative processes using the parallel method…
In this paper we study iterative algorithms for finding a common element of the set of fixed points of $\kappa$-strict pseudocontractions or finding a solution of a variational inequality problem for a monotone, Lipschitz continuous…
This paper is a continuation to the study of generalized quasi contractive operators, essentially due to Akhtar et al. [A multi-step implicit iterative process for common fixed points of generalized C^{q}-operators in convex metric spaces,…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
The purpose of this paper is to introduce two new classes of accelerated distributed proximal conjugate gradient algorithms for multi-agent constrained optimization problems; given as minimization of a function decomposed as a sum of M…
We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…
We study a fixed point iterative method based on generalized relaxation of strictly quasi-nonexpansive operators. The iterative method is assembled by averaging of strings, and each string is composed of finitely many strictly…
In this paper, we develop a new type of accelerated algorithms to solve some classes of maximally monotone equations as well as monotone inclusions. Instead of using Nesterov's accelerating approach, our methods rely on a so-called…
The aim of this article is to introduce an iterative algorithm for finding a common solution from the set of an equilibrium point for a bifunction and the set of a singularity of an inclusion problem on an Hadamard manifold. We also discuss…
We give properties of strict pseudocontractions and demicontractions defined on a Hilbert space, which constitute wide classes of operators that arise in iterative methods for solving fixed point problems. In particular, we give necessary…
We consider the monotone inclusion problems in real Hilbert spaces. Proximal splitting algorithms are very popular technique to solve it and generally achieve weak convergence under mild assumptions. Researchers assume the strong conditions…
In this paper, we introduce a system of split variational inequality problems in real Hilbert spaces. Using projection method, we propose an iterative algorithm for the system of split variational inequality problems. Further, we prove that…
In this paper, we introduce new implicit and explicit iterative schemes which converge strongly to a unique solution of variational inequality problems for strongly accretive operators over a common fixed point set of finite family of…
In this paper, we propose new extragradient algorithms for solving a split equilibrium and nonexpansive mapping SEPNM($C, Q, A, f, g, S, T)$ where $C, Q$ are nonempty closed convex subsets in real Hilbert spaces $\mathcal{H}_1,…
In this work, we develop a convergence framework for iterative algorithms whose updates can be described by a one-parameter family of nonexpansive operators. Within the framework, each step involving one of the main algorithmic operators is…
In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first…
Low rank matrix approximation is a popular topic in machine learning. In this paper, we propose a new algorithm for this topic by minimizing the least-squares estimation over the Riemannian manifold of fixed-rank matrices. The algorithm is…
The concept of asymptotically nonexpansive mappings is an important generalization of the class of nonexpansive mappings. Implicit midpoint procedures are extremely fundamental for solving equations involving nonlinear operators. This paper…