An Algorithm for Solutions of Hammerstein Integral Equations with Maximal Monotone Operators in Classical Banach Spaces
M. O. Uba *
Department of Mathematics, University of Nigeria, Nsukka, Nigeria.
M. A. Onyido
Department of Mathematics, University of Nigeria, Nsukka, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Let X = lp , 2 ≤ p < ∞. Let F : X → X* and K : X* → X be bounded maximal monotone mappings such that the Hammerstein equation u+KFu = 0 has a solution. An explicit iteration sequence is constructed and proved to converge strongly to a solution of this equation. Our method of proof is also of independent interest.
Keywords: Bounded maximal monotone mappings, hammerstein equations; strong convergence