Theorem 1.2 Assume that g ECla, b If the range of the mapping y=y(r) satisfies y∈,列 for all a∈[,,then g has a fixed point in a, b (1.3) Furthermore, suppose that g(a)is defined over(a, b) and that a positive constant K 1 exists with Ig()s K<1 for all c E(a, b), then g has a(1.4 unique fixed point P in a, 6