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Abstract and Applied Analysis
Volume 2015 (2015), Article ID 627260, 7 pages
http://dx.doi.org/10.1155/2015/627260
Research Article

A New Method for Proving Existence Theorems for Abstract Hammerstein Equations

1African University of Science and Technology, Abuja 900241, Nigeria
2Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849-5168, USA
3Department of Mathematical Sciences, Bayero University, Kano 700241, Nigeria

Received 11 December 2014; Accepted 23 February 2015

Academic Editor: Simeon Reich

Copyright © 2015 C. E. Chidume et al. 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

An abstract Hammerstein equation is an equation of the form . A new method is introduced to prove the existence of a solution of this equation where and are nonlinear accretive (monotone) operators. The method does not involve the complicated technique of factorizing a linear map via a Hilbert space and does not involve the use of deep variational techniques.