Common fixed points of an iterative method for Berinde nonexpansive mappings

Abstract

© 2018 by the Mathematical Association of Thailand. All rights reserved. A mapping T form a nonempty closed convex subset C of a uniformly Banach space into itself is called a Berinde nonexpansive mapping if there is L ≥ 0 such that ǁTx – Tyǁ ≤ ǁx – yǁ + Lǁy – Txǁ for any x; y ∈ C. In this paper, we prove weak and strong convergence theorems of an iterative method for approximating common fixed points of two Berinde nonexpansive mappings under some suitable control conditions in a Banach space. Moreover, we apply our results to equilibrium problems and fixed point problems in a Hilbert space.