A fixed point method for stability of involutions on multi-Banach algebraSpringer 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.
Fixed points and Cauchy sequences in semimetric spacesSpringer 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 mappingsSpringer 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.
Periodic solutions for nonresonant parabolic equations on $${\mathbb {R}}^N$$ with Kato–Rellich type potentialsSpringer 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. ...... hiện toàn bộ
Iteration formulae for brake orbit and index inequalities for real pseudoholomorphic curvesSpringer 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.
Multiple solutions of problems with nonlinear first-order differential operatorsSpringer 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.
On scalar field equations with critical nonlinearitySpringer Science and Business Media LLC - Tập 4 - Trang 97-106 - 2008
Kyril Tintarev
The paper concerns existence of solutions to the scalar field equation
(0.1)
$$-\triangle u = f(u),\quad u > 0\,\,\rm{in}\,\,\mathbb{R}^{N},\quad u\,\in\,\mathcal{D}^{1,2}(\mathbb{R}^{N}), N > 2,$$
when the nonlinearity f(s) is of the critical magnitude
...... hiện toàn bộ
Strongly relatively nonexpansive sequences in Banach spaces and applicationsSpringer Science and Business Media LLC - Tập 5 - Trang 201-225 - 2009
Koji Aoyama, Fumiaki Kohsaka, Wataru Takahashi
We introduce the concept of a strongly relatively nonexpansive sequence in a Banach space and investigate its properties. Then we apply our results to the problem of approximating a common fixed point of a countable family of relatively nonexpansive mappings in a uniformly convex and uniformly smooth Banach space.