International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 1, Pages 161-170
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 Rabindranath Sen and Sulekha Mukherjee. 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.
Given that and as nonlinear onto and into self-mappings of a complete metric space , we offer here a constructive proof of the existence of the unique solution of the operator equation , where , by considering the iterative sequence ( prechosen, ). We use Kannan's criterion  for the existence of a unique fixed point of an operator instead of the contraction mapping principle as employed in . Operator equations of the form , where , and positive integers, are also treated.