Related papers: Approaching the maximal monotonicity of bifunction…

In this paper we study the maximal subspaces of continuous n-homogeneous polynomials on complex and real non separable Banach spaces. In the real case we will prove that if P is a 2-homogeneous polynomial and if there exist a k-dimensional…

This paper introduces a new definition of $\alpha$-monotone operators in real 2-uniformly convex and smooth Banach spaces. Based on this new definition, we establish several novel structural and analytical properties of such operators,…

We use techniques of proof mining to extract a uniform rate of metastability (in the sense of Tao) for the strong convergence of approximants to fixed points of uniformly continuous pseudocontractive mappings in Banach spaces which are…

We begin with an improvement to an extension result for subharmonic functions of Blanchet et al. With the aid of this improvement we then give extension results for subharmonic functions, for separately subharmonic functions, for harmonic…

We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…

In this paper, the convergence of alternating minimization is established for non-smooth convex optimization in Banach spaces, and novel rates of convergence are provided. As objective function a composition of a smooth and a non-smooth…

Let $h^\infty_v(\mathbf D)$ and $h^\infty_v(\mathbf B)$ be the spaces of harmonic functions in the unit disk and multi-dimensional unit ball which admit a two-sided radial majorant $v(r)$. We consider functions $v $ that fulfill a doubling…

Let $A$ and $B$ be sets of nonnegative integers. For a positive integer $n$ let $R_{A}(n)$ denote the number of representations of $n$ as the sum of two terms from $A$. Let $\displaystyle s_{A}(x) = \max_{n \le x}R_{A}(n)$ and…

In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions. The first regularity condition we give…

We provide in a unified way quantitative forms of strong convergence results for numerous iterative procedures which satisfy a general type of Fejer monotonicity where the convergence uses the compactness of the underlying set. These…

We extend the idea of approximating piecewise smooth univariate functions using rational approximation introduced in \cite{aka_bas-19a} to two-dimensional space. This article aims to implement the novel piecewise Maehly based…

The paper is devoted to an analysis of optimality conditions for nonsmooth multidimensional problems of the calculus of variations with various types of constraints, such as additional constraints at the boundary and isoperimetric…

In this paper we lay the foundations for the Morse theoretical study of strongly indefinite functionals on Banach manifolds by developing the local theory for a specific model class that captures several key analytical features also arising…

Motivated by open questions in the papers " Refinements and sharpenings of some double inequalities for bounding the gamma function" and "Complete monotonicity and monotonicity of two functions defined by two derivatives of a function…

A new representation is proposed for functions in a Sobolev space with dominating mixed smoothness on an $N$-dimensional hyperrectangle. In particular, it is shown that these functions can be expressed in terms of their highest-order mixed…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

All most all the function spaces over real or complex domains and spaces of sequences, that arise in practice as examples of normed complete linear spaces (Banach spaces), are reflexive. These Banach spaces are dual to their respective…

In this work we derive a convex dual representation for increasing convex functionals on a space of real-valued Borel measurable functions defined on a countable product of metric spaces. Our main assumption is that the functionals fulfill…

This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual can be…

It is well known that many problems in image recovery, signal processing, and machine learning can be modeled as finding zeros of the sum of maximal monotone and Lipschitz continuous monotone operators. Many papers have studied…