Related papers: Maximal monotone operators with non-empty domain i…
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…
In this paper, we construct maximally monotone operators that are not of Gossez's dense-type (D) in many nonreflexive spaces. Many of these operators also fail to possess the Br{\o}nsted-Rockafellar (BR) property. Using these operators, we…
We give a survey on the different regularity properties of sectorial operators on Banach spaces. We present the main results and open questions in the theory and then concentrate on the known methods to construct various counterexamples.
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…
We are concerned with surjectivity of perturbations of maximal monotone operators in non-reflexive Banach spaces. While in a reflexive setting, a classical surjectivity result due to Rockafellar gives a necessary and sufficient condition to…
We study the relations between some geometric properties of maximal monotone operators and generic geometric and analytical properties of the functions on the associate Fitzpatrick family of convex representations. We also investigate under…
This work deals with a maximal monotone operator $A$ of type (D) in a Banach space whose dual space is strictly convex. We establish some representations for the value $Ax$ at a given point $x$ via its values at nearby points of $x$. We…
Previous examples of non-type (D) maximal monotone operators were restricted to $\ell^1$, $L^1$, and Banach spaces containing isometriccopies of these spaces. This fact led to the conjecture that non-type (D) operators were restricted to…
We provide a characterization for maximal monotone realizations for a certain class of (nonlinear) operators in terms of their corresponding boundary data spaces. The operators under consideration naturally arise in the study of…
In this paper we obtain several extension properties for monotone and sublinear operators. The results obtained generalize those known for positive and linear operators.
Fenchel subdifferential operators of lower semicontinuous proper convex functions on real Banach spaces are classically characterized as those operators that are maximally cyclically monotone or, equivalently, maximally monotone and…
The paper is devoted to establishing relationships between global and local monotonicity, as well as their maximality versions, for single-valued and set-valued mappings between finite-dimensional and infinite-dimensional spaces. We first…
We examine the chaotic behavior of certain continuous linear operators on infinite-dimensional Banach spaces, and provide several equivalent characterizations of when these operators have infinite topological entropy. For example, it is…
We provide a concise proof of existence for nonlinear operator equations in separable Banach spaces. Notably, the operator is not assumed to be monotone. Instead, our main hypotheses consist of a continuity assumption and a generalized…
For a discrete dynamics defined by a sequence of bounded and not necessarily invertible linear operators, we give a complete characterization of exponential stability in terms of invertibility of a certain operator acting on suitable Banach…
We present a simple proof of the maximal monotonicity of the subdifferential operator in general Banach spaces. Using the Fitzpatrick function the Rockafellar surjectivity theorem follows as a corollary.
A thorough investigation is made of the optimal domain space of generalized Volterra operators, Ces\`aro operators and other operators when they act in various Banach spaces of analytic functions. Of particular interest is the situation…
Monotone operator theory and fixed point theory for nonexpansive mappings are central areas in modern nonlinear analysis and optimization. Although these areas are fairly well developed, almost all examples published are based on…
Recently, the authors studied the connection between each maximal monotone operator T and a family H(T) of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities. The aim of this…
We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to…