Related papers: Maximal monotone operators with non-maximal graphi…
In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal…
We examine the Maximum Independent Set Problem in an undirected graph. The main result is that this problem can be considered as the solving the same problem in a subclass of the weighted normal twin-orthogonal graphs. The problem is…
We present several sharp upper bounds and some extension for product operators. Among other inequalities, it is shown that if , , are non-negative continuous functions on such that , , then for all non-negative operator monotone decreasing…
We study different geometric properties on infinite graphs, related to the weak-type boundedness of the Hardy-Littlewood maximal averaging operator. In particular, we analyze the connections between the doubling condition, having finite…
A basic idea in optimal transport is that optimizers can be characterized through a geometric property of their support sets called cyclical monotonicity. In recent years, similar "monotonicity principles" have found applications in other…
The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences $(G_n)$ of graphs in terms of a limiting object which may be represented by a symmetric function $W$ on…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
In this paper, the boundedness of some sublinear operators is proved on homogeneous Herz-Morrey spaces with variable exponent.
In this paper maximal commutators and commutators of maximal functions with functions of bounded mean oscillation are investigated. New pointwise estimates for them are proved.
In this paper we {\em discuss} diverse aspects of mutual relationship between adjoints and formal adjoints of unbounded operators bearing a matrix structure. We emphasize on the behaviour of row and column operators as they turn out to be…
Here, we focus on Anderson type operators over infinite graphs where the randomness acts through higher rank perturbations. We show that for special family of graphs, the operator has non-trivial multiplicity for its pure point spectrum.…
We prove the validity of maximum principles for a class of fully nonlinear operators on unbounded subdomains $\Omega \subset \mathbb R^n$ of cylindrical type. The main structural assumption is the uniform ellipticity of the operator along…
A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…
In this note we use recent results concerning the sum theorem for maximal monotone multifunctions in general Banach spaces to find new characterizations and properties of regular maximal monotone multifunctions and then use these to…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
We prove a weak maximum principle for nonlocal symmetric stable operators. This includes the fractional Laplacian. The main focus of this work is the regularity of the considered function.
We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. This operator is perturbed by a first order differential operator, the coefficients of which depend arbitrarily on a…
We study the resolvent norm of a certain class of closed linear operators on a Hilbert space, including unbounded operators with compact resolvent. It is shown that for any point in the resolvent set there exist directions in which the norm…
We study monotone operators in reflexive Banach spaces that are invariant with respect to a group of suitable isometric isomorphisms and we show that they always admit a maximal extension which preserves the same invariance. A similar…
We establish some relationships between an m-accretive operator and its Moore-Penorse inverse. We derive some perturbation result of the Moore-Penorse inverse of a maximal accretive operator. As an application we give a factorization…