  We consider strange attractors of two dimensional generalized map with one
nonlinearity such that Lozi, H\'{e}non and Belykh maps are particular cases of
it. We describe technique of invariant expanding and contracting cones creation
for study of hyperbolic properties. Theorems of singular hyperbolic attractors
for new modifications of Lozi, H\'{e}non and Belykh-type maps are presented.
