Iterative Approximation of Solutions of Hammerstein Integral Equations with Maximal Monotone Operators in Banach Spaces
M. O. Uba *
Department of Mathematics, University of Nigeria, Nsukka, Nigeria.
M. A. Onyido
Department of Mathematics, University of Nigeria, Nsukka, Nigeria.
P. U. Nwokoro
Department of Mathematics, University of Nigeria, Nsukka, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Let X be a uniformly convex and uniformly smooth real Banach space with dual space X*. Let F : X → X* and K : X* → X be bounded maximal monotone mappings. Suppose the Hammerstein equation u + KFu = 0 has a solution. An iteration sequence is constructed and proved to converge strongly to a solution of this equation.
Keywords: Bounded maximal monotone mappings, hammerstein equations, strong convergence.