Generalized Quasilinearization Method and Rapid Convergence for First Order Initial Value Problems

We apply the generalized quasilinearization method of V. Lakshmikantham Nonlinear Anal. 27 1996., 223]227. and the extended method of R. N. Mohapa- tra, K. Vajravelu, and Y. Yin J. Optim. Theory Appl., in press.to the first order initial value problem IVP for short.xX t.sf t, x., x 0.sx0, tgJ with wider class functions f and obtain rapid convergence of monotone sequences which converge uniformly to the unique solution of the IVP.