New approach to the solution of non-linear integral equations via various F Be -contractions

Abstract

In this article, we introduce and establish various approaches related to the F-contraction using new sorts of contractions, namely the extended F Be -contraction, the extended F Be -expanding contraction, and the extended generalized F Be -contraction. Thereafter, we propose a simple and efficient solution for non-linear integral equations using the fixed point technique in the setting of a Be-metric space. Moreover, to address conceptual depth within this approach, we supply illustrative examples where necessary.