Some fixed point results concerning various contractions in extended b- metric space endowed with a graph

Abstract

Contraction type mappings are crucial for understanding fixed point theory under specific conditions. We propose generalized (Boyd–Wong) type A F and (S - N) rational type contractions in an enlarged b-metric space which are represented by a graphically. Also, we gave a contrast of generalized (Boyd–Wong) type A F — contraction in 2D and 3D. We use appropriate illustrations to demonstrate the validity and primacy of our outcomes. Additionally, we use our derived conclusions to solve the Fredholm integral problem.