Argyros, I.K.George, S.2026-02-032025International Journal of Computational Methods, 2025, 22, 2, pp. -2198762https://doi.org/10.1142/S0219876224500518https://idr.nitk.ac.in/handle/123456789/20401The implementation of iterative methods using inverses to solve equations is a computationally expensive or impossible task in general. This is the case, since the analytical form of the inverse is difficult to find in practice. That is why, we replace the inverse by a sum of linear operators which is well defined. The convergence of the resulting hybrid methods is studied based on majorizing sequences under generalized continuity assumptions on the operators involved and in the setting of a Banach space. It is demonstrated by numerical experimentations that the convergence order as well as the number of iterations required to obtain a predetermined error tolerance when comparing the original to the hybrid method is essentially the same. © 2025 World Scientific Publishing Company.Choquet integralInverse problemsIterative methodsMathematical operatorsNonlinear equationsNumerical methodsAnalytical formsConvergence orderErrors toleranceGeneralized EquationsHybrid methodInverseLinear operatorsMajorizing sequencesNumber of iterationsNumerical experimentationsBanach spaces