Results 51 to 60 of about 1,267,876 (189)

Fixed point theorems for F-expanding mappings

Fixed Point Theory and Applications, 2017
Recently, Wardowski (Fixed Point Theory Appl. 2012:94, 2012) introduced a new concept of F-contraction and proved a fixed point theorem which generalizes the Banach contraction principle.
Jarosław Górnicki
doaj   +1 more source

Reduced Assumption in the Banach Contraction Principle [PDF]

Journal of Mathematics and Statistics, 2006
In this study we introduce a novel class of normed spaces called weakly Cauchy normed spaces not necessarily complete in general and proved the existence of a fixed point of contraction mappings in these spaces, this is weaker assumption than the completeness assumption imposed on the given normed space on the other side the contraction condition valid
openaire   +1 more source

A proof of Esterle's conjecture on negative powers of Hilbert‐space contractions

Bulletin of the London Mathematical Society, Volume 58, Issue 9, September 2026.
Abstract We establish the following result, confirming a conjecture of Jean Esterle. For each closed subset E$E$ of the unit circle of Lebesgue measure zero, there exists a positive sequence un→∞$u_n\rightarrow \infty$ with the following property: If T$T$ is a contraction on a Hilbert space such that σ(T)⊂E$\sigma (T)\subset E$ and ∥T−n∥=O(un)$\Vert T^{
Thomas Ransford
wiley   +1 more source

Metric spaces with small rough angles and the rectifiability of rough self‐contracted curves

Journal of the London Mathematical Society, Volume 114, Issue 3, September 2026.
Abstract The small rough angle (SRA$\operatorname{SRA}$) condition, introduced by Zolotov in arXiv:1804.00234, captures the idea that all angles formed by triples of points in a metric space are small. In the first part of the paper, we develop the theory of metric spaces (X,d)$(X,d)$ satisfying the SRA(α)$\operatorname{SRA}(\alpha)$ condition for some
Estibalitz Durand Cartagena, Jeremy T. Tyson   +1 more
wiley   +1 more source

On an abstract nonlinear functional second order Volterra integrodifferential equation

Ratio Mathematica
In this paper, we prove the existence, uniqueness and boundedness of solutions of a nonlinear functional second order Volterra integrodifferential equation in a general Banach space.
Pramod M Dhakane
doaj   +1 more source

Well‐posedness of heat equations with nonlinearities of arbitrarily rapid growth

Proceedings of the London Mathematical Society, Volume 133, Issue 3, September 2026.
Abstract We address local‐ and global‐in‐time well‐posedness of the Cauchy problem for nonlinear heat equations without imposing growth rate restrictions on the nonlinearity a priori. Our results constitute a nontrivial expansion of the classical Lq$L^q$‐theory for nonlinearities dominated by polynomial growth and the exponential‐Orlicz space theory ...
Yohei Fujishima, Kotaro Hisa, Robert Laister   +2 more
wiley   +1 more source

Self‐Similar Blowup for the Cubic Schrödinger Equation

Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1831-1918, August 2026.
ABSTRACT We give a rigorous proof for the existence of a finite‐energy, self‐similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer‐assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation.
Roland Donninger, Birgit Schörkhuber
wiley   +1 more source

Ulam–Hyers stabilities of a differential equation and a weakly singular Volterra integral equation

Journal of Inequalities and Applications, 2021
In this work we study the Ulam–Hyers stability of a differential equation. Its proof is based on the Banach fixed point theorem in some space of continuous functions equipped with the norm ∥ ⋅ ∥ ∞ $\|\cdot \|_{\infty }$ . Moreover, we get some results on
Ozgur Ege, Souad Ayadi, Choonkil Park
doaj   +1 more source

Banach Contraction Principle in Cone Modular Spaces with Banach Algebra

, 2018
10 ...
Özavşar, Muttalip, Çay, Hatice
openaire   +5 more sources

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source