Unified Fixed Point Theory in Generalized Metric Structures with Applications to Nonlinear Economic Systems

This paper introduces a comprehensive framework unifying recent advancements in fixed point theory through the novel concept of twisted weighted Θ-b-metric spaces. We establish a framework of fixed point theorems for multi-valued mappings satisfying generalized rational type contractions that incorporate control functions, weight functions, and twisted admissibility conditions. By synthesizing concepts from {C}iri\'{c}-type contractions, Berinde's almost contractions, Jleli's Θ-contractions, and weighted b-metric spaces, we create a powerful analytical tool with unprecedented theoretical depth. The work provides rigorous proofs, extensive numerical validation, and demonstrates significant applications to economic systems, including production-consumption equilibrium models and fractional economic growth equations. Our results substantially generalize numerous classical theorems while opening new avenues for research in nonlinear analysis and mathematical economics.