Related papers: Additivity, subadditivity and linearity: automatic…
Several subadditivity results and conjectures are given for matrices (or operators), block-matrices, concave functions and norms.
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
Weak submodularity is a natural relaxation of the diminishing return property, which is equivalent to submodularity. Weak submodularity has been used to show that many (monotone) functions that arise in practice can be efficiently maximized…
We investigate the possibility of replacing the topology of convergence in probability with convergence in $L^1$. A characterization of continuous linear functionals on the space of measurable functions is also obtained.
This article introduces a weak pseudo-inverse of a monotone function, which is applied to characterize the associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=t^{[-1]}(F(t(x),t(y)))$ where…
We quantify the uniqueness of continuation from Cauchy or interior data. Our approach consists in extending the existing results in the linear case. As by product we obtain a new stability estimate in the linear case. We also show the…
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…
A compactness of the Revuz map is established in the sense that the locally uniform convergence of a sequence of positive continuous additive functionals is derived in terms of their smooth measures. To this end, we first introduce a metric…
For a subshift $(X, \sigma_X)$ and a subadditive sequence $\mathcal{F}=\{\log f_n\}_{n=1}^{\infty}$ on $X$, we study equivalent conditions for the existence of $h\in C(X)$ such that $\lim_{n\rightarrow\infty}(1/{n})\int \log f_n d \mu=\int…
We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also…
By designating vertices with variables, a simple undirected graph can be augmented to have an associated representing rational function in two variables taking the complex bi-upper halfplane to itself. We give relations between representing…
We consider the Cauchy problem for a semilinear stochastic differential inclusion in a Hilbert space. The linear operator generates a strongly continuous semigroup and the nonlinear term is multivalued and satisfies a condition which is…
The aim of this article is to provide characterizations for subadditivity-like growth conditions for the so-called associated weight functions in terms of the defning weight sequence. Such growth requirements arise frequently in the…
In this paper, we would like to consider the Cauchy problem for a multi-component weakly coupled system of semi-linear $\sigma$-evolution equations with double dissipation for any $\sigma\ge 1$. The first main purpose is to obtain the…
The Cauchy problem for fractional derivatives linear systems of ordinary differential equations with constant coefficients is considered, where at first the analytic expressions are given through the matrix exponent of its corresponding…
In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions objects are…
Our aim is to study the Ulam's problem for Cauchy's functional equations. First, we present some new results about the superstability and stability of Cauchy exponential functional equation and its Pexiderized for class functions on…
We consider the Cauchy problem for homogeneous linear $q$-difference-differential equations with constant coefficients. We characterise convergent, $k$-summable and multisummable formal power series solutions in terms of analytic…
Over the last two decades, submodular function maximization has been the workhorse of many discrete optimization problems in machine learning applications. Traditionally, the study of submodular functions was based on binary function…
The purpose of this article is twofold. First, an issue of regularity of weak solution to the problem $(P)$ (See below) is addressed. Secondly, we investigate the question of $H^s$ versus $C^0$- weighted minimizers of the functional…