Iterative approximation of solutions of equations of Hammerstein type in certain Banach spaces

作者：Chidume C E^*; Shehu Y

来源：Applied Mathematics and Computation, 2013, 219(10): 5657-5667.

DOI：10.1016/j.amc.2012.11.041

• Accretive operators
• Duality maps
• Equations of Hammerstein type
• Modulus of smoothness
• Uniformly Gateaux differentiable norm

Let E be a q-uniformly smooth real Banach space. For each i = 1, 2,... m, let F-i, K-i : E -> E be bounded and accretive mappings. Assume that the generalized Hammerstein equation u + Sigma(m)(i-1) K(i)F(i)u = 0 has a solution in E. Our purpose in this paper is to construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the generalized Hammerstein equation. Our result generalizes and extends the results of Chidume and Ofoedu (2011) [C. E. Chidume, E.U. Ofoedu, Solution of nonlinear integral equations of Hammerstein type, Nonlinear Anal. 74 (2011) 4293-4299] and Chidume and Shehu (2012) [C. E. Chidume, Y. Shehu, Approximation of solutions of generalized equations of Hammerstein type, Comput. Math. Appl. 63 (2012) 966-974]. Numerical example of our result is also included.

• 出版日期2013-1-15