Some Fixed Point Theorems of Generalized Contractions with Application to Boundary Value Problem

In this contribution, our primary aim is to introduce the definition of \(\left( \eta , \pi , \theta \right) \) -generalized rational contraction for three self-maps, followed by an investigation into the existence of coincidence points and the uniqueness of common fixed points in a complete metric space with a partial order. To substantiate our main results, we present relevant examples and discuss their implications. Additionally, we leverage our findings to prove the existence theorem for common solutions of integral equations. Through this study, we contribute to the understanding of these fundamental concepts and provide valuable insights into their applications.