A strong convergence theorem for maximal monotone operators in Banach spaces with applications


 Chidume, C. E.,  DE Souza, G. S.,  Romanus, O. M. and  Nnyaba, U. V.


Abstract

carpathian_2020_36_2_229_240_abstract

An algorithm is constructed to approximate a zero of a maximal monotone operator in a uniformly convex and uniformly
smooth real Banach space. The sequence of the algorithm is proved to converge strongly to a zero of the maximal monotone map.
In the case where the Banach space is a real Hilbert space, our theorem complements the celebrated proximal point algorithm  of Martinet and Rockafellar. Furthermore, our convergence theorem is applied to approximate a solution of a Hammerstein  integral equation  in our general setting. Finally, numerical experiments are presented to illustrate the convergence of our  algorithm.

Additional Information

Author(s)

DE Souza, G. S., Nnyaba, U. V., Romanus, O. M., Chidume, C. E.