Summary: We study strong convergence of the proximal point algorithm. It is known that the proximal point algorithm converges weakly to a solution of a maximal monotone operator, but it fails to converge strongly. Then, in [Math. Program. 87, No. 1(A), 189–202 (2000; Zbl 0971.90062
)], M. V. Solodov
and B. F. Svaiter
introduced the new proximal-type algorithm to generate a strongly convergent sequence and established a convergence property for it in Hilbert spaces. Our purpose is to extend Solodov and Svaiter’s result to more general Banach spaces. Using this, we consider the problem of finding a minimizer of a convex function.