Values of , , and for Example 3.2.

In the realm of b-metric spaces, this study introduces a novel generalized Wardowski-type quasi-contraction, denoted as β-(θ, ϑ). We begin by applying this new contraction to derive standard fixed point results. Subsequently, we establish the existence of a generalized quasi-contraction of the Wardowski type, thereby validating the robustness of our findings. Specifically, we utilize Nadler’s work to model biological ecosystems and apply our results to solve an optimization problem. To illustrate the practical implications and effectiveness of our approach, we provide a comparative analysis between our results and those of Nadler. This comprehensive study underscores the significance and utility of our generalized contraction in both theoretical and applied contexts.