Results 71 to 80 of about 10,513 (300)

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
openaire   +3 more sources

Random Chemostats with Competition and Different Kinetics to Investigate the Growth of the Gut Microbiome

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, Felipe Rivero, Carlos R. Takaessu Jr.   +2 more
wiley   +1 more source

Rate of convergence by Kantorovich-Szász type operators based on Brenke type polynomials

Journal of Inequalities and Applications, 2017
The present paper deals with the approximation properties of the univariate operators which are the generalization of the Kantorovich-Szász type operators involving Brenke type polynomials.
Tarul Garg, Purshottam Narain Agrawal, Serkan Araci   +2 more
doaj   +1 more source

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.
openaire   +5 more sources

Hölder Regularity of the Solutions of Fredholm Integral Equations on Upper Ahlfors Regular Sets

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We extend to the context of metric measured spaces, with a measure that satisfies upper Ahlfors growth conditions, the validity of (generalized) Hölder continuity results for the solution of a Fredholm integral equation of the second kind. Here we note that upper Ahlfors growth conditions include also cases of nondoubling measures.
Massimo Lanza de Cristoforis, Manuel Norman   +1 more
wiley   +1 more source

Superposition operator problems of Hölder-Lipschitz spaces

Demonstratio Mathematica
Let ff be a function defined on the real line, and Tf{T}_{f} be the corresponding superposition operator which maps hh to Tf(h){T}_{f}\left(h), i.e., Tf(h)=f∘h{T}_{f}\left(h)=f\circ h. In this article, the sufficient and necessary conditions such that Tf{
Niu Yeli, Wang Heping
doaj   +1 more source

Influence of Lipschitz bounds on the speed of global optimization

Technological and Economic Development of Economy, 2012
Global optimization methods based on Lipschitz bounds have been analyzed and applied widely to solve various optimization problems. In this paper a bound for Lipschitz function is proposed, which is computed using function values at the vertices of a ...
Remigijus Paulavičius, Julius Žilinskas   +1 more
doaj   +1 more source

Peak Sets for Lipschitz Functions [PDF]

Proceedings of the American Mathematical Society, 1978
We study the peak sets for the algebras of functions analytic in the unit disc D and satisfying a Lipschitz condition on ∂
Novinger, W. P., Oberlin, D. M.
openaire   +2 more sources

Factorization of Lipschitz operators on Banach function spaces

, 2018
[EN] Let (X,d) be a pointed metric space. Let T : X ¿ Y1(µ) and S : X ¿ Y2(µ) be two Lipschitz operators into two Banach function spaces Y1 and Y2 over the same finite measure µ.
Yahi, R., D. Achour, R. Yahi, Achour, D., E. Dahia, Rueda, P., Sánchez Pérez, Enrique Alfonso, P. Rueda, E. A. Sánchez Pérez, Dahia, E.   +9 more
core   +1 more source

Existence of Solution for Two Classes of Quasilinear Systems Defined on a Nonreflexive Orlicz–Sobolev Spaces

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This paper proves the existence of nontrivial solution for two classes of quasilinear systems of the type −ΔΦ1u=Fu(x,u,v)+λRu(x,u,v)inΩ−ΔΦ2v=−Fv(x,u,v)−λRv(x,u,v)inΩu=v=0on∂Ω$$ \left\{\begin{array}{l}\hfill -{\Delta}_{\Phi_1}u={F}_u\left(x,u,v\right)+\lambda {R}_u\left(x,u,v\right)\kern0.1832424242424242em \mathrm{in}\kern0.3em \Omega ...
Lucas da Silva, Marco Souto
wiley   +1 more source