Graph Convergence for the $$H(\cdot ,\cdot )$$ H ( · , · ) -Co-accretive Mapping with an Application

2014 ◽  
Vol 38 (4) ◽  
pp. 1481-1506 ◽  
Author(s):  
R. Ahmad ◽  
M. Akram ◽  
M. Dilshad
Keyword(s):  
Accretive Mapping ◽  
Graph Convergence

scholarly journals Homogenization of Maximal Monotone Vector Fields via Selfdual Variational Calculus

2011 ◽  
Vol 11 (2) ◽  
Author(s):  
Nassif Ghoussoub ◽  
Abbas Moameni ◽  
Ramón Zárate Sáiz
Keyword(s):  
Vector Fields ◽  
Maximal Monotone ◽  
Variational Calculus ◽  
Classical Case ◽  
Divergence Form ◽  
Graph Convergence ◽  
Monotone Vector Fields ◽  
Γ Convergence ◽  
Maximal Monotone Vector Fields ◽  
Periodic Family

AbstractWe use the theory of selfdual Lagrangians to give a variational approach to the homogenization of equations in divergence form, that are driven by a periodic family of maximal monotone vector fields. The approach has the advantage of using Γ-convergence methods for corresponding functionals just as in the classical case of convex potentials, as opposed to the graph convergence methods used in the absence of potentials. A new variational formulation for the homogenized equation is also given.

scholarly journals NOTES ON GRAPH-CONVERGENCE FOR MAXIMAL MONOTONE OPERATORS

2010 ◽  
Vol 83 (1) ◽  
pp. 22-29 ◽  
Author(s):  
FILOMENA CIANCIARUSO ◽  
GIUSEPPE MARINO ◽  
LUIGI MUGLIA ◽  
HONG-KUN XU
Keyword(s):  
Monotone Operator ◽  
Maximal Monotone Operator ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Null Sequence ◽  
Graph Convergence ◽  
Common Domain

AbstractWe construct a sequence {An} of maximal monotone operators with a common domain and converging, uniformly on bounded subsets, to another maximal monotone operator A; however, the sequence {t−1nAn} fails to graph-converge for some null sequence {tn}.

scholarly journals A finer singular limit of a single-well Modica–Mortola functional and its applications to the Kobayashi–Warren–Carter energy

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yoshikazu Giga ◽  
Jun Okamoto ◽  
Masaaki Uesaka
Keyword(s):  
Materials Science ◽  
Dimensional Space ◽  
Singular Limit ◽  
Explicit Representation ◽  
Arc Length ◽  
Convergence In Measure ◽  
One Dimensional ◽  
Graph Convergence ◽  
Single Well

Abstract An explicit representation of the Gamma limit of a single-well Modica–Mortola functional is given for one-dimensional space under the graph convergence which is finer than conventional L 1 L^{1} -convergence or convergence in measure. As an application, an explicit representation of a singular limit of the Kobayashi–Warren–Carter energy, which is popular in materials science, is given. Some compactness under the graph convergence is also established. Such formulas as well as compactness are useful to characterize the limit of minimizers of the Kobayashi–Warren–Carter energy. To characterize the Gamma limit under the graph convergence, a new idea which is especially useful for one-dimensional problems is introduced. It is a change of parameter of the variable by arc-length parameter of its graph, which is called unfolding by the arc-length parameter in this paper.

Pointwise topological convergence and topological graph convergence of set-valued maps

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2779-2785
Author(s):  
L. Holá ◽  
G. Kwiecińka
Keyword(s):  
Topological Spaces ◽  
Topological Graph ◽  
Graph Convergence ◽  
Topological Convergence ◽  
Topological Limit ◽  
Graph Limit

Let X,Y be topological spaces and {Fn : n ? ?} be a sequence of set-valued maps from X to Y with the pointwise topological limit G and with the topological graph limit F. We give an answer to the question from ([19]): which conditions on X,Y and/or {F,G,Fn : n ? ?} are needed to F = G.

scholarly journals The Meir-Keeler Type for Solving Variational Inequalities and Fixed Points of Nonexpansive Semigroups in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Phayap Katchang ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Strong Convergence Theorem ◽  
Accretive Mapping ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Nonexpansive Semigroups ◽  
Strongly Accretive Mapping

The aim of this paper is to introduce a new iterative scheme for finding common solutions of the variational inequalities for an inverse strongly accretive mapping and the solutions of fixed point problems for nonexpansive semigroups by using the modified viscosity approximation method associate with Meir-Keeler type mappings and obtain some strong convergence theorem in a Banach spaces under some parameters controlling conditions. Our results extend and improve the recent results of Li and Gu (2010), Wangkeeree and Preechasilp (2012), Yao and Maruster (2011), and many others.

scholarly journals Convergence of steepest descent approximation for set-valued quasi-accretive mapping equations

2000 ◽  
Vol 32 (10) ◽  
pp. 1083-1093 ◽  
Author(s):  
N.-J. Huang ◽  
Y.J. Cho ◽  
M.-R. Bai ◽  
S.M. Kang
Keyword(s):  
Steepest Descent ◽  
Accretive Mapping
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