On iterative solution of nonlinear functional equations in a metric space

Rabindranath Sen and Sulekha Mukherjee

International Journal of Mathematics and Mathematical Sciences, 1983, vol. 6, 1-10

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 A u = P u , where u ∈ R , by considering the iterative sequence A u n + 1 = P u n ( u 0 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 A n u = P m u , where u ∈ R , n and m positive integers, are also treated.

Date: 1983
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:767826

DOI: 10.1155/S0161171283000149

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