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We study the budget map and the indirect utility function of a parametric consumer problem in a Banach space setting by some advanced tools from set-valued and variational analysis. The Lipschitz-likeness and differentiability properties of…

Optimization and Control · Mathematics 2018-04-30 Vu Thi Huong , Jen-Chih Yao , Nguyen Dong Yen

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized…

Machine Learning · Computer Science 2025-03-05 Qi Ye

We construct a Banach rearrangement invariant norm on the measurable space for which the finiteness of this norm for measurable function (random variable) is equivalent to suitable tail (heavy tail and light tail) behavior. We investigate…

Functional Analysis · Mathematics 2012-10-04 E. Ostrovsky , L. Sirota

The aim of this paper is to emphasize various concepts of dichotomies for evolution equations in Banach spaces, due to the important role they play in the approach of stable, instable and central manifolds. The asymptotic properties of the…

Classical Analysis and ODEs · Mathematics 2010-02-08 Codruta Stoica

We study semiflows satisfying a certain squeezing condition with respect to a quadratic functional in some Banach space. Under certain compactness assumptions from our previous results it follows that there exists an invariant manifold,…

Dynamical Systems · Mathematics 2020-11-03 Mikhail Anikushin

The method of compatible sequences is introduced in order to produce non-trivial (closed) invariant subspaces of (bounded linear) operators. Also a topological tool is used which is new in the search of invariant subspaces: the extraction…

Functional Analysis · Mathematics 2007-05-23 George Androulakis

As objects of study in functional analysis, Hilbert spaces stand out as special objects of study as do nuclear spaces in view of a rich geometrical structure they possess as Banach and Frechet spaces, respectively. On the other hand, there…

Functional Analysis · Mathematics 2013-10-29 M A Sofi

The use of anisotropic Banach spaces has provided a wealth of new results in the study of hyperbolic dynamical systems in recent years, yet their application to specific systems is often technical and difficult to access. The purpose of…

Dynamical Systems · Mathematics 2018-10-17 Mark F. Demers

Recently the first author studied the bifurcation of critical points of families of functionals on a Hilbert space, which are parametrised by a compact and orientable manifold having a non-vanishing first integral cohomology group. We…

Differential Geometry · Mathematics 2014-03-19 Alessandro Portaluri , Nils Waterstraat

The theory of Banach spaces of Dirichlet series has drawn an increasing attention in the recent 25 years. One of the main interest of this new theory is that of defining analogues of the classical spaces of analytic functions on the unit…

Complex Variables · Mathematics 2024-03-12 Carlos Gómez-Cabello , Pascal Lefèvre , Hervé Queffélec

Assuming the existence of a general nonuniform dichotomy for the evolution operator of a non-autonomous ordinary linear differential equation in a Banach space, we establish the existence of invariant stable manifolds for the semiflow…

Dynamical Systems · Mathematics 2009-06-01 António J. G. Bento , César Silva

In this paper, some existence results for sign-changing critical points of locally Lipschitz functionals in real Banach space are obtained by the method combining the invariant sets of descending ow method with a quantitative deformation.…

Analysis of PDEs · Mathematics 2024-04-26 Xian Xu , Baoxia Qin

We study in this paper a forward-backward-forward dynamical system for solving a mixed variational inequality problem in a real Hilbert space. For the convergence analysis of our proposed system, we apply the Lyapunov analysis to obtain the…

Optimization and Control · Mathematics 2025-11-25 Chidi Elijah Nwakpa , Chinedu Izuchukwu , Chibueze Christian Okeke

The artefact is dedicated towards the inspection of nonlinear fractional differential systems involving Riemann-Liouville derivative with higher order and fixed lower limit, including non-instantaneous impulses for existence and uniqueness…

Dynamical Systems · Mathematics 2022-07-29 Lavina Sahijwani , N. Sukavanam

In this paper an autonomous analytical system of ordinary differential equations is considered. For an asymptotically stable steady state x0 of the system a gradual approximation of the domain of attraction DA is presented in the case when…

Dynamical Systems · Mathematics 2011-02-19 E. Kaslik , A. M. Balint , St. Balint

A strong inspiration for studying Sobolev type fractional evolution equations comes from the fact that have been verified to be useful tools in the modeling of many physical processes. We introduce a novel technique for solving Sobolev type…

Analysis of PDEs · Mathematics 2021-02-23 Nazim I. Mahmudov , Arzu Ahmadova , Ismail T. Huseynov

We study the existence of positive eigenvalues with associated nonnegative mild eigenfunctions for a class of abstract initial value problems in Banach spaces with functional, possibly nonlocal, initial conditions. The framework includes…

Classical Analysis and ODEs · Mathematics 2026-01-01 Gennaro Infante , Paola Rubbioni

An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local'…

Functional Analysis · Mathematics 2018-09-07 Niushan Gao , Denny H. Leung , Foivos Xanthos

Geodesic contraction in vector-valued differential equations is readily verified by linearized operators which are uniformly negative-definite in the Riemannian metric. In the infinite-dimensional setting, however, such analysis is…

Dynamical Systems · Mathematics 2022-08-12 Anand Srinivasan , Jean-Jacques Slotine

This article gives a new proof of the fundamental lemma of the "weakly admissible implies admissible" theorem of Colmez-Fontaine that describes the semi-stable p-adic representations. To this end, we introduce the category of spectral…

Number Theory · Mathematics 2016-11-01 Jérôme Plût