Extended Newton-like Midpoint Method for Solving Equations in Banach Space

In this study, we present a convergence analysis of Newton-like midpoint method for solving nonlinear equations in Banach space setting. The semilocal is analyzed two different ways. first one shown by replacing the existing conditions with weaker and tighter continuity conditions, thereby enhancing its applicability. second uses more general ?-continuity majorizing principle. This approach includes only order Fréchet derivative applicable problems that were otherwise hard to solve using approaches seen literature. Moreover, local established along existence uniqueness region solution. useful Engineering Applied Science problems. paper ends numerical examples show applicability our theorems cases not covered earlier studies.