Argyros, I.K.George, S.Regmi, S.Argyros, C.I.2026-02-042024Algorithms, 2024, 17, 4, pp. -https://doi.org/10.3390/a17040154https://idr.nitk.ac.in/handle/123456789/21187Iterative algorithms requiring the computationally expensive in general inversion of linear operators are difficult to implement. This is the reason why hybrid Newton-like algorithms without inverses are developed in this paper to solve Banach space-valued nonlinear equations. The inverses of the linear operator are exchanged by a finite sum of fixed linear operators. Two types of convergence analysis are presented for these algorithms: the semilocal and the local. The Fréchet derivative of the operator on the equation is controlled by a majorant function. The semi-local analysis also relies on majorizing sequences. The celebrated contraction mapping principle is utilized to study the convergence of the Krasnoselskij-like algorithm. The numerical experimentation demonstrates that the new algorithms are essentially as effective but less expensive to implement. Although the new approach is demonstrated for Newton-like algorithms, it can be applied to other single-step, multistep, or multipoint algorithms using inverses of linear operators along the same lines. © 2024 by the authors.Iterative methodsMathematical operatorsNonlinear equationsAlgorithm for solvingConvergenceFinite sumsFixed sum of operatorFrechet derivativeHybrid-newton-like algorithmIterative algorithmLinear operatorsNewton-like algorithmSolving nonlinear equationsBanach spaces