... in Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1988.16 D. Guo, V. Lakshmikantham, and X. Liu, Nonlinear Integral Equations in Abstract Spaces, vol. 373 of Mathematics ... Method in Nonlinear Analysis, Shandong Scientific Technical Press, Jinan, China,2000.15 D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, vol. 5 of Notes and Reports in Mathematics ... have 0 ≤ αn0< 1. Thus the Banach contraction mapping principleimplies that A n0has a unique fixed point x∗ in CI,andso A has a unique fixed pointx∗ in CI; by the definition of A, ...