Some applications of Maia's fixed point theorem for Fredholm integral equation systems

Darius Filip

doi:10.24193/subbmath.2022.1.14

Some applications of Maia's fixed point theorem for Fredholm integral equation systems

Authors

Darius Filip Babes-Bolyai University

DOI:

https://doi.org/10.24193/subbmath.2022.1.14

Keywords:

space of continuous functions, vector-valued metric, matrix convergent to zero, $A$-contraction, fixed point, Picard operator, weakly Picard operator, integral equation, Fredholm integral equation system, vectorial Maia's fixed point theorem

Abstract

The aim of this paper is to study the existence and uniqueness of solutions for some Fredholm integral equation systems by applying the vectorial form of Maia's fixed point theorem. Some abstract Gronwall lemmas are also obtained.