F -contractions in w -multiplicative modular metric spaces with an application

In this paper, we extend the fixed point framework introduced by Wardowski by formulating a broader class of F -contractions within the setting of w -multiplicative modular metric spaces. By relaxing certain conditions on both the self-mapping and the auxiliary function, we establish a new fixed point theorem that strictly generalizes existing results in the literature. We further demonstrate the strength and flexibility of our results through a nontrivial example in which the mapping does not satisfy the Banach contraction condition but still admits a unique fixed point under our F -contractive framework. Finally, we present an application to nonlinear Hammerstein-type integral equations, proving the existence and uniqueness of solutions via the proposed theory. A numerical illustration demonstrates the applicability and effectiveness of the method. This study contributes to the advancement of fixed point theory in generalized metric spaces and opens up new directions for solving nonlinear problems in analysis.