Solution of nonlinear integral equations of Hammerstein type

Let E be a 2 -uniformly real Banach space and F , K : E → E be nonlinear-bounded accretive operators. Assume that the Hammerstein equation u + K F u = 0 has a solution. A new explicit iteration sequence is introduced and strong convergence of the sequence to a solution of the Hammerstein equation is...

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Bibliographic Details
Published in:Nonlinear analysis 2011-09, Vol.74 (13), p.4293-4299
Main Authors: Chidume, C.E., Ofoedu, E.U.
Format: Article
Language:English
Subjects:
Accretive operators
Banach space
Convergence
Equations of Hammerstein type
Exact sciences and technology
Generalized duality maps
Integral equations
Mathematical analysis
Mathematics
Modulus of smoothness
Nonlinearity
Operators
Sciences and techniques of general use
Uniformly Gâteaux differentiable norm
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Summary:Let E be a 2 -uniformly real Banach space and F , K : E → E be nonlinear-bounded accretive operators. Assume that the Hammerstein equation u + K F u = 0 has a solution. A new explicit iteration sequence is introduced and strong convergence of the sequence to a solution of the Hammerstein equation is proved. The operators F and K are not required to satisfy the so-called range condition. No invertibility assumption is imposed on the operator K and F is not restricted to be an angle-bounded (necessarily linear) operator.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2011.02.017