Related papers: Marginable functions on Fr\'echet spaces
A real arithmetic function f is multiplicatively monotonous if f (mn) -- f (m) has constant sign for m, n positive integers. Properties and examples of such functions are discussed, with applications to positive hermitian…
In this paper, we give one possible definition for functions of several variables applied to endomorphisms of finite dimensional C-vector spaces. This definition is consistent with the usual notion of a function of a square matrix. Some…
Strong geodesic convex function and strong monotone vector field of order $m$ on Riemannian manifolds have been established. A characterization of strong geodesic convex function of order $m$ for the continuously differentiable functions…
We prove that, any problem of minimization of proper lower semicontinuous function defined on a normal Hausdorff space, is canonically equivalent to a problem of minimization of a proper weak * lower semicontinuous convex function defined…
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions,…
We introduce a notion of variable quasi-Bregman monotone sequence which unifies the notion of variable metric quasi-Fej\'er monotone sequences and that of Bregman monotone sequences. The results are applied to analyze the asymptotic…
These lecture notes for a graduate course cover generalized derivative concepts useful in deriving necessary optimality conditions and numerical algorithms for nondifferentiable optimization problems in inverse problems, imaging, and…
We prove surjectivity result in Fr\'echet spaces of Nash-Moser type. That is, with uniform estimates over all semimorms. Our method works for functions which are only continuous and G\^ateaux differentiable like in the recent result of…
Matrix type operators with the off-diagonal decay of polynomial or sub-exponential types are revisited with weaker assumptions concerning row or column estimates, still giving the continuity results for the frame type operators. Such…
We show that the likelihood function for a multinomial vector observed under arbitrary interval censoring constraints on the frequencies or their partial sums is completely log-concave by proving that the constrained sample spaces comprise…
We present a simple geometric construction for smoothing polyhedral utility functions. Keywords: Afriat- Varian theorem, the utility function, the economic indices theory, convex analysis.
For an operator monotone function $f(t)$ on the positive real line, we show the operator monotonicity of the type of the functions $(t-a)(t-b)/(f(t)-f(a))(f^\sharp(t)-f^\sharp(b))$.
This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…
In this short note, we derive an upper estimate of Clarke's subdifferential of marginal functions in Banach spaces. The structure of the upper estimate is very similar to other results already obtained in the literature. The novelty lies on…
In this paper we present some consequences of the description of matrix representations of asymmetric truncated Toeplitz operators acting between finite-dimensional model spaces. In particular, we prove that these operators can be…
We prove a strengthened form of convexity for operator monotone decreasing positive functions defined on the positive real numbers. This extends Ando and Hiai's work to allow arbitrary positive maps instead of states (or the identity map),…
We address the decision problem for a fragment of real analysis involving differentiable functions with continuous first derivatives. The proposed theory, besides the operators of Tarski's theory of reals, includes predicates for…
The abstract version of Struwe's monotonicity trick developed by Jeanjean and Jeanjean-Toland for functionals depending on a real parameter is improved, under suitable assumptions. Besides, all the machinery is extended to the case of…
This article characterizes conjugates and subdifferentials of convex integral functionals over the linear space $\mathcal N^\infty$ of stochastic processes of essentially bounded variation (BV) when $\mathcal N^\infty$ is identified with…
The paper is devoted to the study, characterizations, and applications of variational convexity of functions, the property that has been recently introduced by Rockafellar together with its strong counterpart. First we show that these…