Mathematical Modelling and Analysis (Feb 2024)

A fixed-point type result for some non-differentiable Fredholm integral equations

  • Miguel A. Hernández-Verón,
  • Sukhjit Singh,
  • Eulalia Martínez,
  • Nisha Yadav

DOI
https://doi.org/10.3846/mma.2024.18338
Journal volume & issue
Vol. 29, no. 1

Abstract

Read online

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.

Keywords