Results 211 to 220 of about 2,291,454 (248)

A Universal Inequality for Stability of Coarse Lipschitz Embeddings

Acta Mathematica Sinica, English Series, 2023
Joram Lindenstrauss showed that the Banach space \(c_0\) is a Lipschitz retract of its bidual, and formulated the problem to know if every Banach space is a Lipschitz retract of its bidual [\textit{J. Lindenstrauss}, Mich. Math. J. 11, 263--287 (1964; Zbl 0195.42803)]. Nigel Kalton provided a negative answer to Lindenstrauss' problem [\textit{N.
Dai, Duan Xu, Zhang, Ji Chao, Fang, Quan Qing, Sun, Long Fa, Zheng, Ben Tuo   +4 more
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Lipschitz-Type Stability in Nonsmooth Convex Programs

SIAM Journal on Control and Optimization, 1999
Summary: This paper deals with upper Lipschitzian continuity of the optimal solution to parametrized convex programs with linear equality and inequality constraints and with a convex nondifferentiable objective function. Under quadratic growth conditions for the objective function, some accurate bound for the rate of the upper Lipschitzian continuity ...
Robert Janin, Jacques Gauvin
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Implicit Functions, Lipschitz Maps, and Stability in Optimization

Mathematics of Operations Research, 1994
We present an implicit function theorem for set-valued maps associated with the solutions of generalized equations. As corollaries of this theorem, we derive both known and new results. Strong regularity of variational inequalities and Lipschitz stability of optimization problems are discussed.
Asen L. Dontchev, William W. Hager
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Embedding of Lipschitz stability in flows

Nonlinear Analysis: Theory, Methods & Applications, 1996
The authors continue their work on the problem of the possibility of embedding a diffeomorphism into a flow. Among other things they prove that if a diffeomorphism is \(C^1\) embedded into a flow on a compact connected Riemannian manifold then it is Lipschitz stable if and only if the flow is Lipschitz stable.
Chu, Chin-Ku, Lee, Keon-Hee
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Investigation of the lipschitz stability via limiting equations

Dynamics and Stability of Systems, 1990
Summary: The work is dedicated to an effective method for investigation of the stability of the solutions of ordinary differential equations. The notions of strong Lipschitz stability and strong uniform Lipschitz stability are introduced. Two theorems are proved. The first one contains sufficient conditions under which the strong Lipschitz stability of
Dishliev, A. B., Bajnov, D. D.
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On integral stability and Lipschitz stability of motion

Ukrainian Mathematical Journal, 1997
We establish new conditions of integral stability and uniform Lipschitz stability based on the use of the comparison principle and a matrix-valued Lyapunov function.
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Lipschitz stability for nonlinear volterra integrodifferential systems

Applied Mathematics and Computation, 1988
Consider the nonlinear integro-differential system \[ (1)\quad x'(t)=f(t,x(t))+\int^{t}_{t_ 0}g(t,s,x(s))ds,\quad x(t_ 0)=x_ 0,\quad t_ 0\geq 0, \] and the variational systems \[ y'(t)=f_ x(t,x(t,t_ 0,x_ 0))y(t)+\int^{t}_{t_ 0}g_ x(t,s,x(s,t_ 0,x_ 0))y(s)ds, \] where \(f\in C[J\times R^ n,R^ n]\), \(g\in C[J\times J\times R^ n,R^ n]\), \(f(t,0)=g(t,s,0)
Elaydi, Saber, Rama Mohana Rao, M.
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Lipschitz Stability of the Cauchy and Jensen Equations

Results in Mathematics, 1997
Let \(G\) be a semigroup and let \(E\) be a normed space. Let \(\mathcal F\) be a given set of functions from \(G\) into \(E\), and let \(\widetilde{\mathcal F}\) be a given set of functions from \(G\times G\) into \(E\). The pair \(({\mathcal F},\widetilde{\mathcal F})\) has the double difference property if for every \(f:G\to E\) such that ...
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A Sufficient Condition for Lipschitz Stability of Controlled Invariant Subspaces

Mediterranean Journal of Mathematics, 2009
Peer ...
Peña Carrera, Marta, Puerta Sales, Ferran, Puerta Coll, Xavier   +2 more
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Determining Linear Cracks by Boundary Measurements: Lipschitz Stability

SIAM Journal on Mathematical Analysis, 1996
Let \(\Omega\) be a bounded simply connected domain in \(\mathbb{R}^2\) of class \(C^{2, \alpha}\) (\(\alpha\in (0, 1)\)) satisfying the following properties, where \(L_1\), \(L_2\), and \(M\) are given positive numbers: (i) perimeter of \(\Omega\leq L_1\); (ii) for any \(z\in \partial\Omega\) there exist two circles with radius \(L_2\) tangent at \(z\)
ALESSANDRINI, GIOVANNI, BERETTA E, VESSELLA S.   +2 more
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