Strong convergence of a proximal-type algorithm for an occasionally pseudomonotone operator in Banach spaces
H. K. Pathak, Yeol Je Cho · Fixed Point Theory and Applications · 2012
It is known that the proximal point algorithm converges weakly to a zero of a maximal monotone operator, but it fails to converge strongly. Then, in (Math. Program. 87:189-202, 2000), Solodov and Svaiter introduced the new proximal-type algorithm to generate a strongly convergent sequence and established a convergence property for the algorithm in Hilbert spaces. Further, Kamimura and Takahashi (SIAM J. Optim. 13:938-945, 2003) extended Solodov and Svaiter’s result to more general Banach spaces and obtained strong convergence of a proximal-type algorithm in Banach spaces. In this paper, by introducing the concept of an occasionally pseudomonotone operator, we investigate strong convergence of the proximal point algorithm in Hilbert spaces, and so our results extend the results of Kamimura and Takahashi. MSC: 47H05, 47J25.