Related papers: A note on lineability
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 paper, we present a new smoothing approach to solve general nonlinear complementarity problems. Under the $P_0$ condition on the original problems, we prove some existence and convergence results . We also present an error estimate…
We prove that a linear nonautonomous differential system with nonuniform hyperbolicity on the half line can be expressed as diagonal system with a perturbation which is small enough. Moreover we show that the diagonal terms are contained in…
In this note we study the convergence of recursively defined infinite series. We explore the role of the derivative of the defining function at the origin (if it exists), and develop a comparison test for such series which can be used even…
Explicit expression for quasi-triviality of scalar non-linear PDE is under consideration.
In this paper, general logic-systems and a necessary and sufficient algorithm are used to substantiate significant consequence operator properties. It is shown, among other results, that, in certain cases, (1) if the number of steps in a…
We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.
In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular…
This note presents an interesting counterexample to a basic covering problem.
In the present paper, we consider the solvability of positive solutions of nonlinear integral equations by means of investigating non-linear Markov operators. To solve the problem we find necessary and sufficient condition for the…
Variational regularization and the quasisolutions method are justified for unbounded closed, possibly nonlinear, operators. The argument is quite simple and yields general results.
Let $A,$ $T$ and $B$ be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences $\left\{ A^{n}TB^{n}\right\} $ and…
These informal notes are concerned with sums and averages in various situations in analysis.
The nonlinear geometry of operator spaces has recently started to be investigated. Many notions of nonlinear embeddability have been introduced so far, but, as noticed before by other authors, it was not clear whether they could be…
We prove a super-rigidity result for algebraic representations over complete fields of irreducible lattices in product of groups and lattices with dense commensurator groups. We derive some criteria for non-linearity of such groups.
Here, we give upper and lower bounds on the count of positive integers $n\le x$ dividing the $n$th term of a nondegenerate linearly recurrent sequence with simple roots.
In 2014, Ibrahim M Alabdulmohsin wrote a paper called "Summability Calculus" where he developed a method to generalize sigma notation to non-integer upper bounds. His paper included a theorem, known as Theorem 6.1.1 (denoted here as Lemma…
In this note one tries to venture into a study of some notions, in the context of a (unital) normed algebra, in particular the algebra of operators on a Hilbert space. Namely, one considers ``moving norms'', i.e.\ norming an element minus a…
Some aspects of analysis on disconnected open subsets of the plane with connected fractal boundary are discussed.
We introduce a nonlinear aggregation type classifier for functional data defined on a separable and complete metric space. The new rule is built up from a collection of $M$ arbitrary training classifiers. If the classifiers are consistent,…