Strong convergence of an iterative sequence for maximal monotone operators in a Banach space. (English) Zbl 1064.47068

Kohsaka, Fumiaki; Takahashi, Wataru

Abstr. Appl. Anal. 2004, No. 3, 239-249 (2004).

Authors’ abstract: “We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by S. Kamimura and W. Takahashi in a Hilbert space [J. Approximation Theory 106, No. 2, 226–240 (2000; Zbl 0992.47022)]. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach space.”

Reviewer: Zhang Xian (Xiamen)

MSC:

47J25	Iterative procedures involving nonlinear operators
47H05	Monotone operators and generalizations

Keywords:

maximal monotone operators; strong convergence

Citations:

Zbl 0992.47022