Related papers: Solution of a Nonlinear Integral Equation via New …
In this paper, the existence and uniqueness of the fixed point for the product of two nonlinear operator in Banach algebra is discussed. In addition, an approximation method of the fixed point of hybrid nonlinear equations in Banach…
We introduce a fixed point iteration process built on optimization of a linear function over a compact domain. We prove the process always converges to a fixed point and explore the set of fixed points in various convex sets. In particular,…
In this paper we prove the strong convergence of the explicit iterative process to a common fixed point of the finite family of nonexpansive mappings defined on Hilbert space, which solves the the variational inequality on the fixed points…
We consider the nonstationary iterated Tikhonov regularization in Banach spaces which defines the iterates via minimization problems with uniformly convex penalty term. The penalty term is allowed to be non-smooth to include $L^1$ and total…
This article introduces an innovative mathematical framework designed to tackle non-linear convex variational problems in reflexive Banach spaces. Our approach employs a versatile technique that can handle a broad range of variational…
Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute…
In this paper, first we introduce a new mapping for finding a common fixed point of an infinite family of nonexpansive mappings then we consider iterative method for finding a common element of the set of fixed points of an infinite family…
This paper adopts a highly effective numerical approach for approximating non-linear stochastic Volterra integral equations (NLSVIEs) based on the operational matrices of the Walsh function and the collocation method. The method transforms…
The concept of nonlinear split ordered variational inequality problems on partially ordered vector spaces is a natural extension of linear split vector variational inequality problems on Banach spaces. The results about nonlinear split…
We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discretization coefficients of the variable-order fractional…
By using the Ishikawa iterative algorithm, we approximate the fixed points and the best proximity points of a relatively non expansive mapping. Also, we use the von Neumann sequence to prove the convergence result in a Hilbert space…
We provide a new approach to obtain solutions of certain evolution equations set in a Banach space and equipped with nonlocal boundary conditions. From this approach we derive a family of numerical schemes for the approximation of the…
Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses local Quasi-Newton…
The $m$-point nonlocal problem for the first order differential equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified provided that the operator…
This paper provides a numerical approach for solving the linear stochastic Volterra integral equation using Walsh function approximation and the corresponding operational matrix of integration. A convergence analysis and error analysis of…
Banach's fixed point theorem for contraction maps has been widely used to analyze the convergence of iterative methods in non-convex problems. It is a common experience, however, that iterative maps fail to be globally contracting under the…
A nonlinear equation in a Banach space is written as a linear equation with a linear operator depending on the unknown solution. This method, which we call a global linearization method, differs essentially from the local linearization…
In this article we develop convergence theory for a general class of adaptive approximation algorithms for abstract nonlinear operator equations on Banach spaces, and use the theory to obtain convergence results for practical adaptive…
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…
In this paper, we explain a new Iterative Method-Fixed Point and develop its convergence theory for finding approximate solutions of nonlinear equations in the setting of Banach spaces. First, we discuss the convergence analysis of our…