In this present paper, given a sequence $$T=\{T_{n}\}_{n=2}^{\infty }$$ T = { T n } n = 2 ∞ consisting of positive numbers, we define the $$T_{\delta }$$ T δ -neighbourhood of the function $$f=h+{{\overline{g}}}\in {{\mathcal {H}}}$$ f = h + g ¯ ∈ H is defined as $$\begin{aligned} N_{\delta }(f)= & {} \left\{ G(z)\;:\;G(z)=z+\sum _{n=2}^{\infty }\left( A_{n}z^{n}+\overline{B_{n}}\overline{z^{n}}\right) ,\right. \\&\;\left. ~\sum _{n=2}^{\infty }T_{n}(|a_{n}-A_{n}|+|b_{n}-B_{n}|)\le \delta ,\;\delta \ge 0\right\} . \end{aligned}$$ N δ ( f ) = G ( z ) : G ( z ) = z + ∑ n = 2 ∞ A n z n + B n ¯ z n ¯ , ∑ n = 2 ∞ T n ( | a n - A n | + | b n - B n | ) ≤ δ , δ ≥ 0 . Furthermore, we investigate some problems concerning $$T_{\delta }$$ T δ -neighbourhoods of functions in various classes of analytic functions. The results obtained here are sharp.