Second hankel determinat for certain analytic functions satisfying subordinate condition

In this paper, we introduce and investigate the following subclass 1+1γzf′(z)+λz2f″(z)λzf′(z)+(1-λ)f(z)-1φ(z)0≤λ≤1,γ∈C{0} $$begin{array}{} displaystyle 1+frac{1}{gamma }left(frac{zf'(z)+lambda z{2}f''(z)}{lambda zf'(z)+(1-lambda )f(z)}-1right) prec varphi (z)qquadleft( 0leqlambdaleq 1,g in mathbb{C} smallsetminus{0}right)end{array} $$ of analytic functions, φ is an analytic function with positive real part in the unit disk, satisfying φ (0) = 1, φ '(0) > 0, and φis symmetric with respect to the real axis. We obtain the upper bound of the second Hankel determinant aa a32 $begin{array}{} a2-3 end{array} $ | for functions belonging to the this class is studied using Toeplitz determinants. The results, which are presented in this paper, would generalize those in related works of several earlier authors.