Strong convergence theorem for strict pseudo-contractions in Hilbert spaces

Abstract

Abstract In this paper, inspired by Hussain et al. (Fixed Point Theory Appl. 2015:17, 2015), we study a modified Mann method to approximate strongly fixed points of strict pseudo-contractive mappings. In (Hussain et al. in Fixed Point Theory Appl. 2015:17, 2015) it is shown that the same algorithm converges strongly to a fixed point of a nonexpansive mapping under suitable hypotheses on the coefficients. Here the assumptions on the coefficients are different, as well as the techniques of the proof.

Keywords

• Mann’s iterations
• strict pseudo-contractions mappings
• variational inequalities
• Mainge’s lemma