The Mann and Ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings. (English) Zbl 0939.47053

Chang, Shih Sen

Comput. Math. Appl. 37, No. 9, 17-24 (1999).

The so-called “variational inclusion problem” VIP \((T,A,g,\Phi)\) in a Banach space is the following: for any \(f\in X\) to find an \(u\in X\) such that \(g(u)\in D(\partial\Phi)\), \[ \langle Tu- Au-f, v- g(u)\rangle\geq \Phi(g(u))- \Phi(v), \] for all \(v\in X^*\). (Here \(\partial\Phi\) denotes the subdifferential of \(\Phi\).)
The purpose of this paper is to study the existence and uniqueness of solutions and also the convergence problem of Mann-Ishikawa iterative processes for a class of accretive VIP.

Reviewer: A.Petrusel (Cluj-Napoca)

MSC:

47J20	Variational and other types of inequalities involving nonlinear operators (general)
47J25	Iterative procedures involving nonlinear operators
47H99	Nonlinear operators and their properties
49J40	Variational inequalities
65K10	Numerical optimization and variational techniques
47H06	Nonlinear accretive operators, dissipative operators, etc.

Keywords:

accreative mapping; Mann-Ishikawa iterative processes; variational inclusion problem

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