Related papers: Maximally Monotone Linear Subspace Extensions of M…
In this paper, we survey recent progress on the theory of maximally monotone operators in general Banach space. We also extend various of the results and leave some open questions.
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…
In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental…
In this work, we propose a new existence result for quasi-equilibrium problems using generalized monotonicity in an infinite dimensional space. Also, we show that the notions of generalized monotonicity can be characterized in terms of…
The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
We study the problem of extending an order-preserving real-valued Lipschitz map defined on a subset of a partially ordered metric space without increasing its Lipschitz constant and preserving its monotonicity. We show that a certain type…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
In this paper we describe a novel a procedure to build a linear order from an arbitrary poset which (i) preserves the original ordering and (ii) allows to extend monotonic and antitonic mappings defined over the original poset to monotonic…
This paper concerns generalized differential characterizations of maximal monotone set-valued mappings. Using advanced tools of variational analysis, we establish coderivative criteria for maximal monotonicity of set-valued mappings, which…
The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximal monotone operators provided that Rockafellar's constraint qualification holds. In this note, we provide a new maximal…
Singular chain spaces for linear relations in linear spaces play a fundamental role in the decomposition of linear relations in finite-dimensional spaces. In this paper singular chains and singular chain spaces are discussed in detail for…
We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…
Maximally monotone operators play important roles in optimization, variational analysis and differential equations. Finding zeros of maximally monotone operators has been a central topic. In a Hilbert space, we show that most resolvents are…
Monotone operators are of basic importance in optimization as they generalize simultaneously subdifferential operators of convex functions and positive semidefinite (not necessarily symmetric) matrices. In 1970, Asplund studied the additive…
It is shown that, for maximally monotone linear relations defined on a general Banach space, the monotonicities of dense type, of negative-infimum type, and of Fitzpatrick-Phelps type are the same and equivalent to monotonicity of the…
In this paper, we develop some of the theory of SSD spaces and SSDB spaces, and deduce some results on maximally monotone multifunctions on a reflexive Banach space.
In this paper we present some new results on the existence of solutions of generalized variational inequalities in real reflexive Banach spaces with Fr\'echet differentiable norms. Moreover, we also give some theorems about the structure of…
The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximal monotone operators due to Minty. In this paper, we systematically…
This paper is primarily concerned with the problem of maximality for the sum $A+B$ and composition $L^{*}ML$ in non-reflexive Banach space settings under qualifications constraints involving the domains of $A,B,M$. Here $X$, $Y$ are Banach…