A strong convergence theorem for maximal monotone operators in Banach spaces with applications
C.E. Chidume, Geraldo Soares de Souza, O. M. Romanus, U. V. Nnyaba · Carpathian Journal of Mathematics · 2020
An algorithm is constructed to approximate a zero of a maximal monotone operator in a uniformly convex anduniformly smooth real Banach space. The sequence of the algorithm is proved to converge strongly to a zeroof the maximal monotone map. In the case where the Banach space is a real Hilbert space, our theorem com-plements the celebrated proximal point algorithm of Martinet and Rockafellar. Furthermore, our convergencetheorem 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.