Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 6 (2011), 117 -- 126


Safeer Hussain Khan

Abstract. In this paper, we introduce a generalized iteration scheme with errors for convergence to common fixed points of two nonexpansive mappings. This scheme contains a wide variety of existing iteration schemes as its special cases. The main feature of this scheme is that its special cases can handle both strong convergence like Halpern-type and weak convergence like Ishikawa-type iteration schemes. Our main theorem will in particular generalize a recent result by Kim and Xu [9].

2010 Mathematics Subject Classification: 47H10; 54H25.
Keywords: Generalized iteration scheme; Common fixed point; Nonexpansive mapping; Weak convergence; Strong convergence.

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Safeer Hussain Khan
Department of Mathematics, Statistics and Physics, Qatar University,
Doha 2713, State of Qatar.