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...
| Authors: | , , , |
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| 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 |
| 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. |
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