Exploring Novel Fixed Point Solutions in Boundary Value Problems

Within this manuscript, we present an innovative concept of contraction, building upon the foundation laid by Jleli and Samet. Subsequently, we introduce the concept of θ-contractions. Leveraging these novel ideas, we formulate a series of fresh fixed-point theorems applicable to spaces utilizing the Controlled Branciari metric. Notably, our approach integrates and consolidates diverse fixed-point outcomes, eliminating the necessity for the Hausdorff assumption. To illustrate the practicality of our findings, we provide examples and applications to boundary value problems associated with fourth-order differential equations.