CONVEXITY OF THE SET OF FIXED POINTS OF A QUASI-PSEUDOCONTRACTIVE TYPE LIPSCHITZ MAPPING AND THE SHRINKING PROJECTION METHOD

Abstract

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.