A Fixed-Point Type Result for Some Non-Differentiable Fredholm Integral Equations

[EN] In this paper, we present a new fixed-point result to draw conclusions about the existence and uniqueness of the solution for a nonlinear Fredholm integral equation of the second kind with non -differentiable Nemytskii operator. To do this, we will transform the problem of locating a fixed poin...

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Bibliographic Details
Authors: Hernández-Verón, Miguel A., Singh, Sukhjit, Yadav, Nisha, Martínez Molada, Eulalia|||0000-0003-2869-4334
Format: article
Publication Date:2024
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/205460
Online Access:https://riunet.upv.es/handle/10251/205460
Access Level:Open access
Keyword:Fixed point theorem
Global convergence
Fredholm integral equations
Derivative-free iterative processes
Description
Summary:[EN] In this paper, we present a new fixed-point result to draw conclusions about the existence and uniqueness of the solution for a nonlinear Fredholm integral equation of the second kind with non -differentiable Nemytskii operator. To do this, we will transform the problem of locating a fixed point for an integral operator into the problem of locating a solution of an integral equation. Thus, assuming conditions on the Nemytskii operator, we will obtain a global convergence domain for the solution of the considered integral equation, taking for this a uniparametric family of derivativefree iterative processes with quadratic convergence. This result provides us a new fixed-point result for the integral operator considered.