Taiwanese Journal of Mathematics

ON THE PROJECTION DYNAMICAL SYSTEMS IN BANACH SPACES

Ya. I. Alber and Jen-Chih Yao

Full-text: Open access

Abstract

We study dynamical systems of the projection gradient type for convex constrained minimization problems, clearance type dynamical system for fixed point problems with nonexpansive self-mappings and descent-like dynamical system for variational inequalities with maximal monotone operators in Banach spaces. We prove the weak convergence of dynamical trajectories and establish the estimates of the convergence rate with respect to functionals of the problems. We also produce some strong convergence theorem. The results presented in the paper are new even in Hilbert spaces.

Article information

Source
Taiwanese J. Math., Volume 11, Number 3 (2007), 819-847.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404760

Digital Object Identifier
doi:10.11650/twjm/1500404760

Mathematical Reviews number (MathSciNet)
MR2340166

Zentralblatt MATH identifier
1174.49004

Subjects
Primary: 46T 37C 37C25: Fixed points, periodic points, fixed-point index theory 34G20: Nonlinear equations [See also 47Hxx, 47Jxx] 47H
Secondary: 37L 47J

Keywords
Banach spaces duality mappings minimization and fixed point problems dynamical systems metric and generalized projections gradient of functional clearance operator and clearance functional weak convergence convergence with respect to functionals

Citation

Alber, Ya. I.; Yao, Jen-Chih. ON THE PROJECTION DYNAMICAL SYSTEMS IN BANACH SPACES. Taiwanese J. Math. 11 (2007), no. 3, 819--847. doi:10.11650/twjm/1500404760. https://projecteuclid.org/euclid.twjm/1500404760


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