We perform the investigation of positives and negatives of the three-step iterative frozen-type Newton-like method for solving nonlinear equations in a Banach space. We perform a local convergence analysis by the Taylor expansion and study semilocal convergence by using the recurrence relations technique under the conditions of Kantorovich theorem for Newton’s method. The convergence results are examined by comparing the proposed method with the Newton method and the fourth-order Jarratt method by using some test functions. We discuss the corresponding conjugacy maps for quadratic polynomials along with the extraneous fixed points. Additionally, the theoretical and numerical results are examined by using the dynamical analysis of a selected test function. This not only confirms the theoretical and numerical results but also reveals some drawbacks of the frozen-type Newton-like method.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 2, pp. 233–252, February, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i2.6764.
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Singh, M.K., Singh, A.K. Study of Frozen-Type Newton-Like Method in a Banach Space with Dynamics. Ukr Math J 74, 266–288 (2022). https://doi.org/10.1007/s11253-022-02063-9
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DOI: https://doi.org/10.1007/s11253-022-02063-9