Reckoning Common Fixed Point of Enriched Pseudocontractive Mappings: An Iterative Approach

Abstract

We extend the notion of (a, k)-enriched strictly pseudocontractive mappings to the notion of the more general aenriched pseudocontractive mappings. It is shown with examples that the class of a-enriched pseudocontractive mappings is more general than the classes of (a, k)-enriched strictly pseudocontractive and pseudocontractive mappings. Some fundamental properties of the class a-enriched pseudocontractive mappings are proved. In particular, it is shown that the fixed point set of certain class of a-enriched pseudocontractive self-mappings of a nonempty closed convex subset of a real Hilbert space is closed and convex. Demiclosedness property of such class of a-enriched pseudocontractive mappings is proved. Certain strong convergence theorems are then proved for the iterative approximation of fixed points of the class a-enriched pseudocontractive mappings.