A bounded linear operator $T$ on a Hilbert space $mathfrak{H}$ isconvex, if $$|mathfrak{T}^{2}v|^2-2|mathfrak{T}v|^2+|v|^2 geq 0.$$ In this paper, sufficient conditions to hypercyclicity of adjoint of unilateral (bilateral) forward (backward) weighted shift operator is given. Also, we present some example of convex operators such that it's adjoint is hypercyclic. Finally, the spectrum of convex multiplication operators is obtained and an example of convex, multiplication operators is given such that it's adjoint is hypercyclic.