相关论文: An application of continuous logic to fixed point …

The concept of metastable convergence was identified by Tao;it allows converting theorems about convergence into stronger theorems about uniform convergence. The Uniform Metastability Principle (UMP) states that if $T$ is a theorem about…

Recently, the different types of unbounded convergences (uo, un, uaw, uaw*) in Banach lattices were studied. In this paper, we study the continuous functionals with respect to unbounded convergences. We first characterize the continuity of…

We develop an adiabatic theory for generators of contracting evolution on Banach spaces. This provides a uniform framework for a host of adiabatic theorems ranging from unitary quantum evolutions through quantum evolutions of open systems…

This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due…

The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem…

In this work, we address unconstrained finite-sum optimization problems, with particular focus on instances originating in large scale deep learning scenarios. Our main interest lies in the exploration of the relationship between recent…

We establish fixed point theorems for nonlinear contractions on a metric space (not essentially complete) endowed with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those…

In this paper we study the behavior of finite dimensional fixed point iterations, induced by discretization of a continuous fixed point iteration defined within a Banach space setting. We show that the difference between the discrete…

The regularity theory of the Campanato space $\mathcal{L}^{(q,\lambda)}_k(\Omega)$ has found many applications within the regularity theory of solutions to various geometric variational problems. Here we extend this theory from…

An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\alpha$-maxmin nonlinear…

We present a constructive proof of Tychonoff's fixed point theorem in a locally convex space for sequentially locally non-constant functions, As a corollary to this theorem we also present Schauder's fixed point theorem in a Banach space…

Unsteady Lifting-Line Theory (ULLT) is a low order method capable of modeling interacting unsteady and finite wing effects at low computational cost. Most formulations of the method assume inviscid flow and small amplitudes. Whilst these…

In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence…

We introduce and study a new class of nonlinear monotone operators acting in normal cones of real Banach spaces and possessing the property of strong concavity. We establish new constructive principles for the existence of nonzero fixed…

We articulate here a series of specific metagoals designed to address the challenge of creating AGI systems that possess the ability to flexibly self-modify yet also have the propensity to maintain key invariant properties of their goal…

The relationship between geometric and variational principles remains central to Nonlinear Analysis. This paper introduces the \textbf{Orbit-Summability Fixed Point Criterion}, a novel, purely dynamical condition, and establishes its…

This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved…

A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of…

We focus on the persistence principle over weak interpretability logic. Our object of study is the logic obtained by adding the persistence principle to weak interpretability logic from several perspectives. Firstly, we prove that this…

Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint…