IJPAM: Volume 80, No. 2 (2012)
ITERATIVE ALGORITHMS OF KIRK-NOOR TYPE WITH
ERRORS IN AN ARBITRARY BANACH SPACE
Department of Mathematics
Rohtak, 124001, INDIA
Abstract. The purpose of this paper is to introduce a new hybrid fixed point iterative algorithm of Kirk-Noor type with errors and to establish a general theorem to approximate the unique common fixed point of three operators satisfying a certain contractive condition in an arbitrary Banach space using the algorithms of Kirk-Noor type with errors. We use a more general contractive condition and prove a convergence theorem under weaker conditions on parameters than those of Rashwan et al. (2009). Our results, therefore, are improvements, generalization and extensions of the works of Rhoades (1976), Berinde (2004), Rashwan et al. (2009) and many others in the literature. An example to illustrate the validity of our results is also provided.
Received: April 24, 2012
AMS Subject Classification: 47H06, 54H25
Key Words and Phrases: Kirk type iterative schemes, quasi-contractive operators
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395