A Four-Step Semi-Implicit Midpoint Approximation Scheme for Fixed Point with Applications (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.
Keywords: Semi-implicit midpoint approximation; fixed point; convergence and stability; quasi-variational inequality; nonlinear fractional differential equation