Initial Time Difference Quasilinearization Method in Banach Space

Abstract

In this paper, the method of the quasilinearization technique in Banach space is applied to obtain upper and lower sequences with initial time difference in terms of the solutions of the linear differential equations that start at different initial times. It is also shown that these sequences converge to the unique solution of the nonlinear equation in Banach space uniformly and superlinearly.