Random Fixed Points using Random Sehgal Contraction in Separable Complete Metric Spaces with Applications

In this manuscript, we investigate random fixed points by examining random mappings that satisfy random Sehgal-type inequalities within the framework of separable complete metric spaces.  The principal contributions of this study both encompass and significantly broaden a range of existing results in the pertinent literature.  There is a novel approach to finding the random fixed points as the proposed results in the random setting. To demonstrate the effectiveness and strength of our results, we also provide illustrative examples. Moreover, the results are also applied to Ulam Hyers Stability (UHS) and the Limit Shadowing Properties (LSP) of random fixed point problems. Subsequently, we utilize the derived results to systematically consolidate and affirm the existence and uniqueness of random solutions for nonlinear random Fredholm integral equations.