Algorithm for approximating solutions of Hammerstein integral equations with maximal monotone operators

2017 ◽  
Vol 48 (3) ◽  
pp. 391-410 ◽  
Author(s):  
M. O. Uba ◽  
M. I. Uzochukwu ◽  
M. A. Onyido
Keyword(s):  
Integral Equations ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Hammerstein Integral Equations

scholarly journals Approximation of zeros of m-accretive mappings, with applications to Hammerstein integral equations

2020 ◽  
Vol 36 (1) ◽  
pp. 59-69
Author(s):  
CHARLES CHIDUME ◽  
GERALDO SOARES De SOUZA ◽  
VICTORIA UKAMAKA NNYABA
Keyword(s):  
Real Hilbert Space ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Accretive Operator ◽  
Hammerstein Integral Equation ◽  
Proximal Point ◽  
Hammerstein Integral Equations ◽  
Uniformly Smooth ◽  
Accretive Mappings

"An algorithm for approximating zeros of m-accretive operators is constructed in a uniformly smooth real Banach space. The sequence generated by the algorithm is proved to converge strongly to a zero of an m-accretive operator. In the case of a real Hilbert space, our theorem complements the celebrated proximal point algorithm of Martinet and Rockafellar for approximating zeros of maximal monotone operators. Furthermore, the convergence theorem proved is applied to approximate a solution of a Hammerstein integral equation. Finally, numerical experiments are presented to illustrate the convergence of our algorithm."

scholarly journals Topological degree and application to a parabolic variational inequality problem

2001 ◽  
Vol 25 (4) ◽  
pp. 273-287 ◽  
Author(s):  
A. Addou ◽  
B. Mermri
Keyword(s):  
Variational Inequality ◽  
Topological Degree ◽  
Variational Inequality Problem ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Parabolic Variational Inequality ◽  
Inequality Problem ◽  
Monotone Map ◽  
New Formulation

We are interested in constructing a topological degree for operators of the formF=L+A+S, whereLis a linear densely defined maximal monotone map,Ais a bounded maximal monotone operators, andSis a bounded demicontinuous map of class(S+)with respect to the domain ofL. By means of this topological degree we prove an existence result that will be applied to give a new formulation of a parabolic variational inequality problem.

scholarly journals Theoretical Study of a Chain Sliding on a Fixed Support

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
Jérôme Bastien ◽  
Claude-Henri Lamarque
Keyword(s):  
Dry Friction ◽  
Theoretical Study ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Rheological Models ◽  
Implicit Euler Scheme ◽  
Linear Spring ◽  
A Chain ◽  
Uniqueness Theory

A chain sliding on a fixed support, made out of some elementary rheological models (dry friction element and linear spring) can be covered by the existence and uniqueness theory for maximal monotone operators. Several behavior from quasistatic to dynamical are investigated. Moreover, classical results of numerical analysis allow to use a numerical implicit Euler scheme.

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