LAUSR

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