Opuscula Math. 34, no. 1 (2014), 67-79
http://dx.doi.org/10.7494/OpMath.2014.34.1.67

Opuscula Mathematica

# Approximating fixed points of a countable family of strict pseudocontractions in Banach spaces

Prasit Cholamjiak

Abstract. We prove the strong convergence of the modified Mann-type iterative scheme for a countable family of strict pseudocontractions in $$q$$-uniformly smooth Banach spaces. Our results mainly improve and extend the results announced in [Y. Yao, H. Zhou, Y.-C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J. Appl. Math. Comput. 29 (2009), 383-389].

Keywords: common fixed points, convergence theorem, modified Mann iteration, strict pseudocontractions, $$q$$-uniformly smooth Banach spaces.

Mathematics Subject Classification: 47H09, 47H10.

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• Prasit Cholamjiak
• University of Phayao, School of Science, Phayao 56 000, Thailand
• Revised: 2013-05-17.
• Accepted: 2013-05-24.