Quadruple Controlled Metric-Type Spaces with Fixed-Point Results and Applications to Boundary Value Problem

In this paper, we introduce a novel class of quadruple controlled metric-type spaces formulated in a four-dimensional setting. Within this framework, we extend the notion of a Θ-contraction mapping to accommodate such spaces. By employing these concepts, we establish several new fixed-point theorems that significantly generalize and enhance the existing results in the literature. The validity and effectiveness of the proposed approach are demonstrated through carefully constructed illustrative examples within the defined space and for the derived fixed-point results. Finally, an application to a boundary value problem is presented, highlighting the potential of the developed theory. Furthermore, a coupled four-component thermo-chemical system was examined as an additional application, demonstrating the broader applicability of the proposed framework.