The titled Carathodory class and its applications

This survey mainly deals with the tilted Carath{é}odory class by angle $λ$ (denoted by $\mathcal{P}_λ$) an element of which maps the unit disc into the tilted right half-plane $\{w: \Re e^{iλ} w>0\}$. Firstly we will characterize $\mathcal{P}_λ$ from different aspects. In section 3, various estimates of functionals over $\mathcal{P}_λ$ are deduced from the known corresponding estimates of $\mathcal{P}_{0}$ or elementary functional analysis. Finally some subsets of analytic functions related to $\mathcal{P}_λ$ including close-to-convex functions with argument $λ$, $λ$-spirallike functions, $λ$-Robertson functions and analytic functions whose derivative is in $\mathcal{P}_λ$ are also considered as applications

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