Results 61 to 70 of about 9,704 (289)
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar +3 more
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Embedding with a Lipschitz function
Random Structures & Algorithms, 2005 AbstractWe investigate a new notion of embedding of subsets of {−1,1}n in a given normed space, in a way which preserves the structure of the given set as a class of functions on {1, …, n}. This notion is an extension of the margin parameter often used in Nonparametric Statistics.
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Lipschitz Functions and Spectral Synthesis [PDF]
Proceedings of the American Mathematical Society, 1981 An S S -set in the circle group
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Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
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On the reduced-set pareto-lipschitzian optimization
Computational Science and Techniques, 2013 A well-known example of global optimization that provides solutions within fixed error limits is optimization of functions with a known Lipschitz constant. In many real-life problems this constant is unknown.
Jonas Mockus, Remigijus Paulavičius
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Regularity of Lipschitz Functions on the Line
Real Analysis Exchange, 2003 The authors note a gap in Sciffer's construction of an everywhere irregular Lipschitz function of the real line and give their own construction. The Dini derivatives are denoted by \(D^+\), \(D_+\), \(D^-\), \(D_-\). The Clarke derivatives are \(S^+f(x)=\limsup_{y\to x+,h\to0}(f(y+h)-f(y))/h\), \(S_+f(x)=\liminf_{y\to x+,h\to0}(f(y+h)-f(y))/h\), \(S^-f(
Preiss, David, Rolland, Louise
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We investigate some chemostat models incorporating wall growth, competition, random fluctuations on the dilution rate, and different consumption functions (Monod and Haldane). We analyze the asymptotic behavior of the solutions of the corresponding random differential systems to establish conditions on the model parameters under which the ...
Javier López‐de‐la‐Cruz +2 more
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On the extremal semi-Lipschitz functions
Journal of Numerical Analysis and Approximation Theory, 2002 The extremal elements of the unit balls of Banach spaces play an important role in the study of the geometry of the space as well as in various applications.
Costică Mustăţa
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Density of Lipschitz functions in energy
Calculus of Variations and Partial Differential Equations, 2022 AbstractIn this paper, we show that the density in energy of Lipschitz functions in a Sobolev space$$N^{1,p}(X)$$N1,p(X)holds for all$$p\in [1,\infty )$$p∈[1,∞)whenever the spaceXis complete and separable and the measure is Radon and positive and finite on balls. Emphatically,$$p=1$$p=1is allowed.
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Essentially Smooth Lipschitz Functions
, 1997 In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on separable Banach spaces. For example, we examine the relationship between integrability,D-representability,
Moors, Warren B., Borwein, Jonathan M.
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