Let $mathcal{A}$ be the class of analytic functions f in the open unit disk $mathbb{U}$={z : ${mid}z{mid}$ < 1} with the normalization conditions $f(0)=f^{prime}(0)-1=0$. If $f(z)=z+sum_{n=2}^{infty}a_nz^n$ and ${delta}$ > 0 are given, then the $T_{delta}$-neighborhood of the function f is defined as $$TN_{delta}(f){g(z)=z+sum_{n=2}^{infty}b_nz^n{in}mathcal{A}:sum_{n=2}^{infty}T_n{mid}a_n-b_n{mid}{leq}{delta}}$$, where $T={T_n}_{n=2}^{infty}$ is a sequence of positive numbers. In the present paper we investigate some problems concerning $T_{delta}$-neighborhoods of function in various classes of analytic functions with $T={2^{-n}/n^2}_{n=2}^{infty}$. We also find bounds for $^{delta}^*_T(A,B)$ defined by $$^{delta}^*_T(A,B)=jnf{{delta}>0:B{subset}TN_{delta}(f);for;all;f{in}A}$$ where A, B are given subsets of $mathcal{A}$.