The recent neutron scattering experiments in high T-c superconductors show that the frequencies of the LO phonon of a stretching mode is strongly softened and the frequencies of the LO and TO phonons are inverted in certain wave number and frequency regions. This fact suggests that the electronic dielectric function becomes negative (over-screening effect) due to the correlation effect in these regions, and the Coulomb interaction in the LO phonon is screened. In this case, the theory suggests that the attractive interaction mediated by optical phonons is highly enhanced. This fact will be a capable mechanism of high T-c superconductivity. A characteristic of the electronic energy band in cuprate superconductors is that there appear the flat bands just below the Fermi level along the k(x) and k(y) axes due to the correlation effect. This feature has been observed by the angle-resolved photoemissions. From both the above effects, we predict that the symmetry of the order parameter is of the d(x2-y2) wave and the superconduting transition temperature can exceeds 200 K. (C) 2002 Elsevier Science B.V. All rights reserved.