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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…

Functional Analysis · Mathematics 2022-01-19 Khaled Ben Amara , Maria Isabel Berenguer , Aref Jeribi

Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…

Optimization and Control · Mathematics 2021-05-18 Patrick L. Combettes , Zev C. Woodstock

In this paper we obtain, by using proof mining methods, quantitative results on the asymptotic regularity of the viscosity approximation method (VAM) with error terms for m-accretive operators in Banach spaces. For concrete instances of the…

Optimization and Control · Mathematics 2024-06-27 Paulo Firmino , Laurentiu Leustean

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…

Functional Analysis · Mathematics 2020-12-29 Koji Aoyama , Yasunori Kimura , Fumiaki Kohsaka

Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…

Functional Analysis · Mathematics 2026-01-12 Nida Izhar Mallick , Izhar Uddin

In this paper, we unify all know iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptotically $I$-nonexpansive mappings. Note that such a scheme…

Functional Analysis · Mathematics 2012-04-10 Farrukh Mukhamedov , Mansoor Saburov

Our aim in this paper is to present results of existence of fixed points for continuous operators in Banach spaces using measure of noncompactness under an integral condition. This results are generalization of results given by A. Aghajania…

Functional Analysis · Mathematics 2015-07-02 Vatan Karakaya , Bouzara Nour El Houda , Kadri Dogan , Yunus Atalan

In this paper, we discuss the construction, analysis and implementation of a novel iterative regularization scheme with general convex penalty term for nonlinear inverse problems in Banach spaces based on the homotopy perturbation…

Numerical Analysis · Mathematics 2018-01-10 Jing Wang , Wei Wang , Bo Han

In this work, we provide conditions for nonlinear monotone semigroups on locally convex vector lattices to give rise to a generalized notion of viscosity solutions to a related nonlinear partial differential equation. The semigroup needs to…

Analysis of PDEs · Mathematics 2025-02-26 Fabian Fuchs , Max Nendel

In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…

Exactly Solvable and Integrable Systems · Physics 2007-11-16 Dan Butnariu , Gabor Kassay

Several non-linear operators in stochastic analysis, such as solution maps to stochastic differential equations, depend on a temporal structure which is not leveraged by contemporary neural operators designed to approximate general maps…

Dynamical Systems · Mathematics 2025-04-11 Luca Galimberti , Anastasis Kratsios , Giulia Livieri

Operator splitting techniques have recently gained popularity in convex optimization problems arising in various control fields. Being fixed-point iterations of nonexpansive operators, such methods suffer many well known downsides, which…

Optimization and Control · Mathematics 2020-04-01 Andreas Themelis , Panagiotis Patrinos

In this work we study integral equations defined on the whole real line. Using a suitable Banach space, we look for solutions which satisfy some certain kind of asymptotic behavior. We will consider spectral theory in order to find fixed…

Classical Analysis and ODEs · Mathematics 2018-11-16 Alberto Cabada , Lucía López-Somoza , F. Adrián F. Tojo

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…

Numerical Analysis · Mathematics 2010-01-12 Michael Holst , Gantumur Tsogtgerel , Yunrong Zhu

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…

Analysis of PDEs · Mathematics 2023-09-12 YR. Bai , S. Migorski , VT. Nguyen , JW. Peng

We introduce and analyze a fast iterative method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. The key idea, in contrast to the standard Landweber method, is to use multiple search directions per…

Numerical Analysis · Mathematics 2018-08-01 Anne Wald

We propose a method to obtain iterative schemes guarantee unique solutions for systems of partial differential equations that are not symmetric with respect to the time by generalizing He variational iteration method and using Banach fixed…

General Mathematics · Mathematics 2019-01-01 Abdulhameed Qahtan Abbood Altai

Smooth Equations of the form G[z]=0 are investigated in Banach spaces with the aim of continuing the basic solution G[0]=0 to a solution curve of G[z]=0 with the implicit function theorem. If the linearization is surjective, then the…

Algebraic Geometry · Mathematics 2019-07-25 Matthias Stiefenhofer

In the present work, we discuss variational regularization for ill-posed nonlinear problems with focus on an oversmoothing penalty term. This means in our model that the searched-for solution of the considered nonlinear operator equation…

Numerical Analysis · Mathematics 2022-11-02 Robert Plato , Bernd Hofmann

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…

Optimization and Control · Mathematics 2022-05-05 Avinash Dixit , D. R. Sahu , Pankaj Gautam , T. Som