Stud. Univ. Babe¸s-Bolyai Math. 63(2018), No. 2, 257–267 DOI: 10.24193/subbmath.2018.2.09 Extending the applicability of modified Newton-HSS method for solving systems of nonlinear equations Janak Raj Sharma, Ioannis K. Argyros and Deepak Kumar Abstract. We present the semilocal convergence of a modified Newton-HSS method to approximate a solution of a nonlinear equation. Earlier studies show convergence under only Lipschitz conditions limiting the applicability of this method. The convergence in this study is shown under generalized Lipschitz- type conditions and restricted convergence domains. Hence, the applicability of the method is expanded. Moreover, numerical examples are also provided to show that our results can be applied to solve equations in cases where earlier study cannot be applied. Furthermore, in the cases where both old and new results are applicable, the latter provides a larger domain of convergence and tighter error bounds on the distances involved. Mathematics Subject Classification (2010): 65F10, 65W05. Keywords: Modified Newton-HSS method, semilocal convergence, system of non- linear equations, generalized Lipschitz conditions, Hermitian method. 1. Introduction Let F : D ⊂ C n → C n be Gateaux-differentiable and D be an open set. Let also x 0 ∈ D be a point at which F 0 (x) is continuous and positive definite. Suppose that F 0 (x)= H(x)+ S(x), where H(x)= 1 2 (F 0 (x)+ F 0 (x) * ) and S(x)= 1 2 (F 0 (x) - F 0 (x) * ) are the Hermitian and Skew-Hermitian parts of the Jacobian matrix F 0 (x), respec- tively. Many problems can be formulated like the equation F (x)=0, (1.1)