Halpern–Ishikawa type iterative method for approximating fixed points of non-self pseudocontractive mappings

Abstract

Abstract In this paper, we define a Halpern–Ishikawa type iterative method for approximating a fixed point of a Lipschitz pseudocontractive non-self mapping T in a real Hilbert space settings and prove strong convergence result of the iterative method to a fixed point of T under some mild conditions. We give a numerical example to support our results. Our results improve and generalize most of the results that have been proved for this important class of nonlinear mappings.

Keywords

• Fixed points
• Monotone mappings
• Pseudocontractive mappings