Certain fixed point results for novel contractions with applications to variational inequalities, economic growth and market equilibrium via fractional differential equations

This paper presents a new approach to analyze the market equilibrium and economic growth via enriched $(\mathring{\mathscr{S}}, \theta , \mathscr{Z})$ -contractions and their generalizations. Developed within normed spaces equipped with binary relations preserving symmetric properties, these classes extend several well-known contractions, including Wardowski’s ${\mathscr{Z}}$ -contractions, Banach contractions, enriched contractions, and $(\theta , {\mathscr{Z}})$ -enriched contractions. The Krasnoselskij iteration method is further refined to incorporate symmetric constraints, enabling the effective identification of fixed points within these spaces. By suitably choosing constants, binary relations, or control functions, our framework extends classical fixed point theorems, with illustrative examples demonstrating its significance and broad applicability. Furthermore, we demonstrate that these constructs enhance the stability of market equilibrium and economic growth models. A Krasnoselskij-type projection algorithm is proposed for variational inequality problems within the class of generalized enriched Bianchini contractions, ensuring existence, uniqueness, and strong convergence of solutions. Numerical experiments confirm its superior stability and faster convergence compared to the classical Picard iteration.