On strongly starlike functions related to the Bernoulli lemniscate.

LetS*_L(λ) be the class of functionsf, analytic in the unit disc Δ ={z:|z|<1}, with the normalization f(0) =f'(0)-1 = 0, which satisfy the conditionz f'(z)/f(z)≺(1 +z)^λ, where≺is the subordination relation. The classS*_L(λ) is a subfamily of the known class of strongly starlike functions of order λ. In this paper, the relations between S*_L(λ) and other classes geometrically defined are considered. Also, we obtain some characteristics such as, bounds for coefficients, radius of convexity, the Fekete-Szeg ?o inequality, logarithmic coefficients and the second Hankel determinant inequality for functions belonging to this class. The univalent functionsfwhich satisfy the condition <{1 +zf"(z)/f'(z)} < 1 +λ/2, (z∈Δ) are also considered here. [ABSTRACT FROM AUTHOR]