Berinde-type generalized $\alpha-\beta-\psi$ contraction in extended $S_{b}$-metric spaces

In this paper, we extend the idea of Berinde-Type generalized $\alpha-\beta-\psi$ contractive mappings in the setting of complete extended $S_{b}$-metric spaces providing a significant advancement in fixed-point theory. The findings extend fixed point theory beyond metric spaces to $S_{b}$-metric spaces, offering a broader range of applications in optimization, nonlinear analysis and mathematical modelling. Non-trivial examples of the findings are provided to validate our claims. These examples demonstrate the potential of the proposed mappings for solving real-world phenomena. The work also suggests intriguing future research directions, such as generalizing fixed-point theorems and applying them to disciplines like dynamical systems and integral equations.