We introduce a new definition of nonlinear mapping, which is called
a quasi-pseudocontractive type mapping, defined on a nonempty closed convex
subset of a real Hilbert space, and we investigate convexity of the set of its fixed
points and approximation of its fixed point. We consider an iterative sequence
generated by the improved hybrid method, also known as the shrinking projection
method, and prove that it converges strongly to a fixed point under some
conditions of the constants for quasi-pseudocontractive type Lipschitz mapping.