An approximate solution of a differential inclusion with maximal monotone operator
Journal of Taibah University for Science, 2020 The theory of differential inclusions has played a central role in many areas as biological systems, physical problems and population dynamics. The principle aim of our work is to compute explicitly the discrete approximate solution of a differential ...
Abdallah Beddani
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A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems [PDF]
Abstract and Applied Analysis, 2010 We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone ...
Siwaporn Saewan, Poom Kumam
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Maximality Theorems on the Sum of Two Maximal Monotone Operators and Application to Variational Inequality Problems [PDF]
Abstract and Applied Analysis, 2016 Let X be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space X⁎. Let T:X⊇D(T)→2X⁎ and A:X⊇D(A)→2X⁎ be maximal monotone operators.
Teffera M. Asfaw
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Optimal Control of Plasticity with Inertia [PDF]
Journal of Nonsmooth Analysis and Optimization, 2021 The paper is concerned with an optimal control problem governed by the equations of elasto plasticity with linear kinematic hardening and the inertia term at small strain.
Stephan Walther
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Maximality of the Sum of a Maximally Monotone Linear Relation and a Maximally Monotone Operator [PDF]
Set-Valued and Variational Analysis, 2013 16 pages.
Borwein, Jonathan M., Yao, Liangjin
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Nontrivial solutions of inclusions involving perturbed maximal monotone operators
Electronic Journal of Differential Equations, 2017 Let X be a real reflexive Banach space and $X^*$ its dual space. Let $L: X\supset D(L)\to X^*$ be a densely defined linear maximal monotone operator, and $T:X\supset D(T)\to 2^{X^*}$, $0\in D(T)$ and $0\in T(0)$, be strongly quasibounded maximal ...
Dhruba R. Adhikari
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Learning Maximally Monotone Operators for Image Recovery [PDF]
SIAM Journal on Imaging Sciences, 2021 We introduce a new paradigm for solving regularized variational problems. These are typically formulated to address ill-posed inverse problems encountered in signal and image processing. The objective function is traditionally defined by adding a regularization function to a data fit term, which is subsequently minimized by using iterative optimization
Jean-Christophe Pesquet +3 more
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Representable Monotone Operators and Limits of Sequences of Maximal Monotone Operators [PDF]
Set-Valued and Variational Analysis, 2011 We show that the lower limit of a sequence of maximal monotone operators on a reflexive Banach space is a representable monotone operator. As a consequence, we obtain that the variational sum of maximal monotone operators and the variational composition of a maximal monotone operator with a linear continuous operator are both representable monotone ...
García, Yboon, Lassonde, Marc
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Maximal monotone operators with non-maximal graphical limit
Examples and Counterexamples, 2022 We present a counterexample showing that the graphical limit of maximally monotone operators might not be maximally monotone. We also characterize the directional differentiability of the resolvent of an operator B in terms of existence and maximal ...
Gerd Wachsmuth
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On the maximal monotonicity and the range of the sum of nonlinear maximal monotone operators [PDF]
Proceedings of the Edinburgh Mathematical Society, 1991 Conditions are given on two maximal monotone (multivalued) operators A and B which ensure that A + B is also maximal. One condition used is that ∥Bx∥≦k(∥x∥)Ax| +d|(A + B)x| + c(∥x∥) for every x∈D(A)⊆D(B), where 0≦k(r)<1, and c(r)≧0 are nondecreasing functions, and 0≦d≦1 is a constant. Here, for a set C, |C| denotes inf{∥y∥:y∈C}.
Webb, J. R. L., Zhao, Weiyu
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