Existence and approximation of solutions of some first order iterative differential equations

Abstract

Existence theorems for some iterative differential equations as well as convergence theorems for a fixed point iterative method designed to approximate these solutions, are proved under weaker conditions than those due to A. Buicǎ ("Existence and continuous dependence of solutions of some functional-differential equations," Seminar on Fixed Point Theory 3, pp. 1-14, 1995). To this end, we basically employ the technique of non-expansive mappings. © 2010 Miskolc University Press.