(untitled) (European Journal of Pure and Applied Mathematics, 2025)
This paper aims to put forward and design a four-step semi-implicit approximation scheme to work out the fixed point of a contractive mapping. Convergence analysis and stability of the proposed scheme is incorporated under some mild assumptions. Finally, the significance and applications of the proposed scheme and theoretical findings are proven by exploring a general quasi-variational inequality and a nonlinear fractional differential equation.