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International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 1, Pages 161-170
http://dx.doi.org/10.1155/S0161171283000149

On iterative solution of nonlinear functional equations in a metric space

1Department of Applied Mathematics, University College of Science, 92 Acharya Prafulla Chandra Road, Calcutta 700009, India
2Department of Mathematics, University of Kalyani, Kalyani, Dt. Nadia, West Bengal, India

Received 4 September 1981

Copyright © 1983 Hindawi Publishing Corporation. 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.

Abstract

Given that A and P as nonlinear onto and into self-mappings of a complete metric space R, we offer here a constructive proof of the existence of the unique solution of the operator equation Au=Pu, where uR, by considering the iterative sequence Aun+1=Pun (u0 prechosen, n=0,1,2,). We use Kannan's criterion [1] for the existence of a unique fixed point of an operator instead of the contraction mapping principle as employed in [2]. Operator equations of the form Anu=Pmu, where uR, n and m positive integers, are also treated.