Revista Colombiana de Matem´ aticas Volumen 55(2021)2, p´ aginas 167-175 New linearization method for nonlinear problems in Hilbert space Nuevo m´ etodo de linealizaci´ on para problemas no lineales en espacios de Hilbert Nada Bouazila 1 , Hamza Guebbai 1, , Wassim Merchela 2 1 Universit´ e 8 Mai 1945, Guelma, Algeria 2 Derzhavin Tambov State University, Tambov, Russia Abstract. In this paper, we build a Newton-like sequence to approach the zero of a nonlinear Fr´ echet differentiable function defined in Hilbert space. This new iterative sequence uses the concept of the adjoint operator, which makes it more manageable in practice compared to the one developed by Kantorovich which requires the calculation of the inverse operator in each iteration. Because the calculation of the adjoint operator is easier compared to the calculation of the inverse operator which requires in practice solving a system of linear equations, our new method makes the calculation of the term of our new sequence easier and more convenient for numerical approximations. We provide an a priori convergence theorem of this sequence, where we use hypotheses equivalent to those constructed by Kantorovich, and we show that our new iterative sequence converges towards the solution. Key words and phrases. Nonlinear problems, Newton-like method, Fr´ echet dif- ferentiability, Adjoint Operator. 2020 Mathematics Subject Classification. 49M15, 49J50. Resumen. En este art´ ıculo, construimos una sucesi´ on similar a la de Newton para acercarnos al cero de una funci´ on diferenciable en el sentido Fr´ echet no lineal definida en un espacio de Hilbert. Esta nueva sucesi´ on utiliza el concepto del adjunto del operador, que hace que el proceso iterativo sea m´as manejable en la pr´ actica en comparaci´ on al desarrollado por Kantorovich que requiere el c´ alculo del operador inverso en cada iteraci´ on. Dado que el c´ alculo del opera- dor adjunto es m´ as f´ acil en comparaci´ on con el c´ alculo del operador inverso que en la pr´ actica equivale a resolver un sistema de ecuaciones, nuestra nuevo 167 https://doi.org/10.15446/recolma.v55n2.102622