In this paper, we present the concept of rational θ ‐Reich and θ ‐Sehgal contraction mappings in usual metric spaces by integrating the classical Reich and Sehgal contractions with Singh’s iterative framework. We establish unified fixed‐point theorems that guarantee existence and uniqueness under both constant and functional parameters. Our proposed rational θ ‐Reich and θ ‐Sehgal formulations provide a comprehensive synthesis of foundational results, including those of Banach, Kannan, and Chatterjea. Furthermore, we provide a rigorous analysis of the Picard iteration’s convergence, offering new insights into the stability and asymptotic behavior of nonlinear operators. The versatility of the proposed framework is demonstrated through its application across diverse domains, including fractal geometry, fractional calculus, and the modeling of financial markets and economic growth trajectories.
Hammad et al. (Thu,) studied this question.