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Solution of nonlinear integral equations of Hammerstein type

✍ Scribed by C.E. Chidume; E.U. Ofoedu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
223 KB
Volume
74
Category
Article
ISSN
0362-546X

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✦ Synopsis

Let E be a 2-uniformly real Banach space and F , K : E β†’ E be nonlinear-bounded accretive operators. Assume that the Hammerstein equation u + KFu = 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.

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