T-NEIGHBORHOODS IN VARIOUS CLASSES OF ANALYTIC FUNCTIONS
T-NEIGHBORHOODS IN VARIOUS CLASSES OF ANALYTIC FUNCTIONS
Let <TEX>$\mathcal{A}$</TEX> be the class of analytic functions f in the open unit disk <TEX>$\mathbb{U}$</TEX>={z : <TEX>${\mid}z{\mid}$</TEX> < 1} with the normalization conditions <TEX>$f(0)=f^{\prime}(0)-1=0$</TEX>. If <TEX>$f(z)=z+\sum_{n=2}^{\infty}a_nz^n$</TEX> and <TEX>${\delta}$</TEX> > 0 are given, then the <TEX>$T_{\delta}$</TEX>-neighborhood of the function f is defined as <TEX>$$TN_{\delta}(f)\{g(z)=z+\sum_{n=2}^{\infty}b_nz^n{\in}\mathcal{A}:\sum_{n=2}^{\infty}T_n{\mid}a_n-b_n{\mid}{\leq}{\delta}\}$$</TEX>, where <TEX>$T=\{T_n\}_{n=2}^{\infty}$</TEX> is a sequence of positive …