Exploring Fixed-Point Results Using Random Sehgal Contraction in Symmetric Random Cone Metric Spaces with Applications

This paper introduces a new concept of random Sehgal contraction in the setting of random cone metric spaces. We explore the modern advancements of traditional fixed-point theorems in a random setting, elaborating on the Sehgal–Guseman fixed-point theorem within the realm of random cone metric spaces. A significant aspect of our research is the interplay between symmetry and randomness; while symmetry provides a framework for understanding structural properties, randomness introduces complexity, which can lead to unexpected behaviors. Our research provides a deeper understanding of the classical results and incorporates a detailed example to illustrate our findings. In addition, major random fixed-point results are also established, which could be applied to nonlinear random fractional differential equations (FDEs) and integral equations as well as to random boundary value problems (BVPs) related to homogeneous random transverse bars.