THE SET OF SOLUTIONS OF VOLTERRA AND URYSOHN INTEGRAL EQUATIONS IN BANACH SPACES

We prove to existence theorems of solutions of nonlinear integral equations of Uryshohn type x(t) = phi(t) + lambda integral(alpha)(0) f(t, s, x(s)) ds and Volterra type x(t) = phi(t) + integral(t)(0) f(t, s, x(s)) ds, t is an element of I-alpha = [0, alpha], alpha, lambda is an element of R-+,R- with the Henstock-Kurzweil-Pettis integral. Moreover, we show that the set S of all solutions of the Volterra integral equation is compact and connected. The assumptions about the function f are really weak: scalar measurability and weak sequential continuity with respect tot the third variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of the measure of weak noncompactness.