### Weak and strong convergence of an iterative algorithm for Lipschitz pseudo-contractive maps in Hilbert spaces

#### Abstract

In this paper, let K be a closed convex subset of a real Hilbert space H and T: K → K a Lipschitz pseudo-contractive map such that F(T) 6= / 0. Let {αn}, {βn} and {γn} be real sequences in (0,1). For x1∈ K, let {xn} be generated iteratively by

xn+1= Pk[(1−αn−γn)xn+γnTyn],

yn= (1−βn)xn+βnTxn,n ≥ 1.

Under some mild conditions on parameters {αn}, {βn}, {γn}, we prove that our new iterative algorithm converges strongly to a fixed point of T. No compactness assumption is imposed on T and no further requirement is imposed on F(T).

**How to Cite this Article:**V.E. Ingbianfam, F.A. Tsav, I.S. Iornumbe, Weak and strong convergence of an iterative algorithm for Lipschitz pseudo-contractive maps in Hilbert spaces, Adv. Fixed Point Theory, 6 (2016), 194-206 Copyright © 2016 V.E. Ingbianfam, F.A. Tsav, I.S. Iornumbe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Fixed Point Theory

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