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A fixed point method for stability of involutions on multi-Banach algebra
Springer Science and Business Media LLC - Tập 22 - Trang 1-11 - 2020
N. Salehi, S. M. S. Modarres
We prove the Hyers–Ulam–Rassias stability of involution on multi-Banach algebra by fixed point method and find some conditions for which a multi-Banach algebra with approximate involution is a $$C^*$$-algebra.
Limiting Bourgain–Brezis estimates for systems of linear differential equations: Theme and variations
Springer Science and Business Media LLC - Tập 15 - Trang 273-297 - 2014
Jean Van Schaftingen
J. Bourgain and H. Brezis have obtained in 2002 some new and surprising estimates for systems of linear differential equations, dealing with the endpoint case L 1 of singular integral estimates and the critical Sobolev space $${W^{1,n}(\mathbb{R}^n)}$$ . This paper presents an overview of the results, further developments over the last ten years and challenging open problems.... hiện toàn bộ
Fixed points and Cauchy sequences in semimetric spaces
Springer Science and Business Media LLC - Tập 17 - Trang 541-555 - 2015
W. A. Kirk, Naseer Shahzad
There have been numerous attempts recently to extend many of the metric standard fixed point theorems to a more general semimetric context. In many instances a weakened form of the triangle inequality is involved and the space is assumed to be complete. Thus Cauchy sequences play a central role. One of the standard tests to determine when a sequence is Cauchy in a metric space (X, d) is the summat... hiện toàn bộ
Best proximity point theorems for contractive mappings
Springer Science and Business Media LLC - Tập 20 - Trang 1-16 - 2018
S. Sadiq Basha
This article is concerned with some new best proximity point theorems for principal cyclic contractive mappings, proximal cyclic contractive mappings, and proximal contractive mappings. As a consequence, an interesting fixed point theorem, due to Edelstein, for a contractive mapping is obtained from all those best proximity point theorems.
Measures of noncompactness in modular spaces and fixed point theorems for multivalued nonexpansive mappings
Springer Science and Business Media LLC - Tập 23 - Trang 1-25 - 2021
T. Domínguez Benavides, P. Lorenzo Ramírez
This paper is devoted to state some fixed point results for multivalued mappings in modular vector spaces. For this purpose, we study the uniform noncompact convexity, a geometric property for modular spaces which is similar to nearly uniform convexity in the Banach spaces setting. Using this property, we state several new fixed point theorems for multivalued nonexpansive mappings in modular space... hiện toàn bộ
Periodic solutions for nonresonant parabolic equations on $${\mathbb {R}}^N$$ with Kato–Rellich type potentials
Springer Science and Business Media LLC - Tập 23 Số 4 - Trang 1-32 - 2021
Ćwiszewski, Aleksander, Łukasiak, Renata
A criterion for the existence of T-periodic solutions of nonautonomous parabolic equation $$u_t = \Delta u + V(x)u + f(t,x,u)$$ , $$x\in {\mathbb {R}}^N$$ , $$t>0$$ , where V is Kato–Rellich type potential and f diminishes at infinity, will be provided. It is proved that, under the nonresonance assumption, i.e. $${\mathrm {Ker}} (\Delta + V)=\{0\}$$ , the equation admits a T-periodic solution. Mor... hiện toàn bộ
Iteration formulae for brake orbit and index inequalities for real pseudoholomorphic curves
Springer Science and Business Media LLC - Tập 24 - Trang 1-30 - 2022
Beijia Zhou
I give precise iteration formulae for brake orbits in dimension 3 and use these formulae to get some index inequalities for moduli spaces of real pseudoholomorphic curves, which are important to establish real embedded contact homology and real cylindrical contact homology in dimension 3.
An approach to the existence and uniqueness of fixed point results in $${\varvec{b}}$$ b -metric spaces via $${\varvec{s}}$$ s -simulation functions
Springer Science and Business Media LLC - Tập 19 Số 4 - Trang 2819-2830 - 2017
Oratai Yamaod, Wutiphol Sintunavarat
Multiple solutions of problems with nonlinear first-order differential operators
Springer Science and Business Media LLC - Tập 17 - Trang 23-42 - 2015
N. El Khattabi, M. Frigon, N. Ayyadi
In this paper, we establish the existence of solutions to firstorder differential equations with nonlinear differential operators satisfying the periodic boundary value or the initial value conditions. Notions of upper and lower solutions are introduced. Multiplicity results are also presented.
Các điểm cố định trong không gian metric có thứ tự với các ứng dụng trong lý thuyết đồng homotopy Dịch bởi AI
Springer Science and Business Media LLC - Tập 20 - Trang 1-15 - 2018
Asma Rashid Butt, Ismat Beg, Aqsa Iftikhar
Trong bài báo này, chúng tôi chứng minh các định lý điểm cố định cho các ánh xạ thỏa mãn một quan hệ ngầm trong không gian metric có thứ tự. Như một ứng dụng, chúng tôi đạt được một kết quả đồng homotopy. Kết quả của chúng tôi chỉnh sửa/mở rộng một số kết quả điểm cố định đã có trong tài liệu nghiên cứu.
#điểm cố định #không gian metric có thứ tự #lý thuyết đồng homotopy #ánh xạ #định lý.
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