Solution of nonlinear integral equations of Hammerstein type |
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Authors: | C.E. Chidume E.U. Ofoedu |
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Affiliation: | a The Abdus Salam International Centre for Theoretical Physics, Trieste, Italyb Department of Mathematics, Nnamdi Azikiwe University, P.M.B. 5025, Awka, Anambra State, Nigeria |
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Abstract: | 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+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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Keywords: | 47H06 47H09 47J05 47J25 |
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