Unified Fixed-Point Theorems for Generalized p-Reich and p-Sehgal Contractions in Complete Metric Spaces with Application to Fractal and Fractional Systems

This paper introduces new generalized forms of contractive mappings in the framework of complete metric spaces. By extending the classical Reich and Sehgal contractions to their iterated counterparts in Singh’s sense, we establish unified fixed-point theorems that ensure both existence and uniqueness under constant and variable contractive parameters. The proposed p-Reich and p-Sehgal contractions encompass several well-known results, including those of Banach, Kannan, Chatterjea, Reich, and Sehgal, as special cases. Convergence of the associated Picard iterative process is rigorously analyzed, revealing deeper insights into the iterative stability and asymptotic behavior of nonlinear mappings in metric spaces. The practical utility of our unified fixed-point theorems is illustrated through concrete applications in fractal and fractional calculus.