A sequence $\{x_{i}\}$ in a metric space $(X,d)$ is said to converge quadratically to $x^{*}$ if there is a constant $1>c>0$ such that $d(x_{i+1},x^{*})\leq cd(x_{i},x^{*})^{2}$ for all $i$.
The convergence is said to be of order $p$ if $d(x_{i+1},x^{*})\leq cd(x_{i},x^{*})^{p}$ for all $i$.