Advances in Rational Contractions within Extended b-Metric Spaces and Their Applications

This study introduces a novel class of rational contractions within the framework of extended b-metric spaces, extending classical fixed point theory to more generalized and flexible settings. We establish new fixed point theorems using a control function approach, which broadens the scope of contractive mappings that can be studied under extended b-metric spaces. The methodology combines analytical techniques with integral operator theory, allowing us to investigate the existence and uniqueness of solutions to both Volterra and Urysohn integral equations. To validate the theoretical results, illustrative examples and numerical simulations are presented, demonstrating the effectiveness and real-world relevance of the proposed framework.