Semilocal convergence of multi-point improved super-Halley-type methods without the second derivative under generalized weak condition

In this paper, we consider the semilocal convergence of multi-point improved super-Halley-type methods in Banach space. Different from the results of super-Halley method studied in reference Gutiérrez, J.M. and Hernández, M.A. (Comput. Math. Appl. 36,1–8, 1998) these methods do not require second derivative of an operator, the R-order is improved and the convergence condition is also relaxed. We prove a convergence theorem to show existence and uniqueness of the solution.

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