Related papers: Weak Convergence Theorem by a New Extragradient Me…
In this paper we propose new averaged iterative algorithms designed for solving a split common fixed-point problem in the class of demicontractive mappings. The algorithms are obtained by inserting an averaged term into the algorithms used…
The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
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…
The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it. Instead of computing exact projections on the constraint…
In this paper, we introduce a new modified Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of relatively nonexpansive mappings in a Banach space. Our results…
We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…
We study the nonexpansivity of reflection mappings in geodesic spaces and apply our findings to the averaged alternating reflection algorithm employed in solving the convex feasibility problem for two sets in a nonlinear context. We show…
We use $KKM$ theorem to prove the existence of a new fixed point theorem for non-expansive mapping:Let M be a bounded closed convex subset of Hilbert space H, and $A:M\rightarrow M$ be a non-expansive mapping, then exists a fixed point of A…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
We propose in this paper a proximal and contraction method for solving a convex mixed variational inequality problem in a real Hilbert space. To accelerate the convergence of our proposed method, we incorporate an inertial extrapolation…
The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We…
In this paper, we introduce a new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. The iterative process is based on two well-known projection method and the hybrid (or…
An interesting observation is that most pairs of weakly homogeneous mappings have no strongly monotonic property, which is one of the key conditions to ensure the unique solvability of the generalized variational inequality. This paper…
The extended Weber location problem is a classical optimization problem that has inspired some new works in several machine learning scenarios recently. However, most existing algorithms may get stuck due to the singularity at the data…
The split common fixed-point problem is an inverse problem that consists in finding an element in a fixed-point set such that its image under a bounded linear operator belongs to another fixed-point set. Recently Censor and Segal proposed…
This paper seeks to advance the theory of nonexpansive mappings by introducing and exploring a novel class of nonexpansive type mappings, which we aptly designate as perimetric nonexpansive mappings. We establish that the collection of…
In this paper, we introduce an inertial proximal method for solving a bilevel problem involving two monotone equilibrium bifunctions in Hilbert spaces. Under suitable conditions and without any restrictive assumption on the trajectories,…
We develop a unified T-extended framework for weakly contractive, weakly Kannan, and Geraghty classes of self-maps S on a metric space (X, d), where distances are measured on the auxiliary image via d(Tx, Ty), and the dynamics is governed…
We propose in this work a subgradient extragradient method with inertial and correction terms for solving equilibrium problems in a real Hilbert space. We obtain that the sequence generated by our proposed method converges weakly to a point…