lipschitz analysis of g-phase retrievable frames

A g-phase retrievable frame is a $lambda$-phase retrievable frame in finite dimensional hilbert space $mathcal{h}_n$, where $lambda$ is an special function, which is called phase coefficient function. in this paper we study the lipschitz analysis of the nonlinear map $alpha_{lambda,{mathcal{f}}}:widehat{mathcal{h}_n}longrightarrowmathbb{f}^m, alpha_{lambda,{mathcal{f}}}(hat{x}):=begin{bmatrix}lambdaleft( leftlangle {x,f_k}rightrangleright)end{bmatrix}_{1leq kleq m}$, where $widehat{mathcal{h}_n}$ is the quotient space corresponding to a special equivalence relation on $mathcal{h}_n$ with respect to phase coefficient function $lambda$,  $mathcal{f}={f_k}_{k=1}^m$ is a $lambda$-phase retrievable frame for $mathcal{h}_n$, $mathbb{f}=mathbb{r}$ for real hilbert space $mathcal{h}_n$ and $mathbb{f}=mathbb{c}$ for complex hilbert space $mathcal{h}_n$.