Existence and uniqueness of solutions in the Lipschitz space of a functional equation and its application to the behavior of the paradise fish

Josefa Caballero, Łukasz Płociniczak and Kishin Sadarangani

Applied Mathematics and Computation, 2024, vol. 477, issue C

Abstract: In this paper, we examine the solvability of a functional equation in a Lipschitz space. As an application, we use our result to determine the existence and uniqueness of solutions to an equation describing a specific type of choice behavior model for the learning process of the paradise fish. Finally, we present some concrete examples where, using numerical techniques, we obtain approximations to the solution of the functional equation. As the straightforward Picard's iteration can be very expensive, we show that an analytical suboptimal least-squares approximation can be chosen in practice, resulting in very good accuracy.

Keywords: Fixed point; Banach fixed point theorem; Lipschitz space; Functional equation; Behavioral sciences (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:477:y:2024:i:c:s0096300324002595

DOI: 10.1016/j.amc.2024.128798

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