The unique solution of boundary value problems for nonlinear second-order integral–differential equations of mixed type in Banach spaces

In this paper, a class of two-point boundary value problems for nonlinear second-order integral–differential equations of mixed type is investigated in a real Banach space without making any compactness type assumption; we establish conditions for the existence of a unique solution of the equation and develop an iterative formula for approximation of the solution and a formula for estimating the error of the iterative solution. The results we obtained generalize and improve various recent results.