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Various iterative methods have been introduced by involving Taylor's series on the auxiliary function g x to solve the nonlinear equation f x = 0 . In this paper, we introduce the expansion of g x with the inclusion of weights w i such that ∑ i = 1 p w i = 1 and knots τ i ∈ 0,1 in order to develop a new family of iterative methods. The methods proposed in the present paper are applicable for different choices of auxiliary function g x , and some already known methods can be viewed as thedoi:10.1155/2020/7356408 fatcat:m3hptfgwmjbjzav5ezzs2syg54