Novel Computational Iterative Methods with Optimal Order for Nonlinear Equations

Table 1

Typical forms of 𝐺(𝑡), 𝐻(𝜏), and 𝐾(𝜑) based on (2.2) where 𝑡=𝑓(𝑦)/𝑓(𝑥), 𝜏=𝑓(𝑦)/𝑓^′(𝑥), 𝜑=𝑓(𝑥)/𝑓^′(𝑥), and 𝜃∈ℝ−{0}.

Forms	Weight function for 𝐺(𝑡)	Weight function for 𝐻(𝜏)	Weight function for 𝐾(𝜑)
1	1+𝑡^2	1+𝜏+𝜃𝜏^2	1+𝜑^2
2	1+𝜃𝑡^3	(1+𝜏)/(1−𝜏)	1+𝜃𝜑^3