Abstract
Let E be a 2-uniformly smooth real Banach space. For each i=1,2,…,m, let Fi,Ki:E→E be bounded and accretive mappings. Assume that the generalized Hammerstein equation u+∑i=1mKiFiu=0 has a solution in E. We construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the generalized Hammerstein equation. Our result improves, generalizes and extends the results of Chidume and Ofoedu [C.E. Chidume, E.U. Ofoedu, Solution of nonlinear integral equations of Hammerstein type, Nonlinear Anal. 74 (2011) 4293–4299] and Chidume and Shehu [C.E. Chidume, Y. Shehu, Approximation of solutions of generalized equations of Hammerstein type, Comput. Math. Appl. 63 (2012) 966–974].
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
