Results 61 to 70 of about 7,649 (300)

Common Fixed Point for Self-Mappings Satisfying an Implicit Lipschitz-Type Condition in Kaleva-Seikkala's Type Fuzzy Metric Spaces

Abstract and Applied Analysis, 2013
We first introduce the new real function class ℱ satisfying an implicit Lipschitz-type condition. Then, by using ℱ-type real functions, some common fixed point theorems for a pair of self-mappings satisfying an implicit Lipschitz-type condition in fuzzy ...
Ming-Liang Song, Xiu-Juan Zhu
doaj   +1 more source

Uniqueness for retarded delay differential equations without Lipschitz condition

Electronic Journal of Qualitative Theory of Differential Equations, 2008
Consider the equation $\dot x(t)=f(t, x(t), x(t-r(t)))$ with the initial condition $x_{0}=\phi$. Here $f$ is a continuous real function, but it does not satisfy other regularity conditions.
M. Bartha, J. Terjéki
doaj   +1 more source

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
wiley   +1 more source

Approximate solutions for a class of doubly perturbed stochastic differential equations

Advances in Difference Equations, 2018
In this paper, we study the Carathéodory approximate solution for a class of doubly perturbed stochastic differential equations (DPSDEs). Based on the Carathéodory approximation procedure, we prove that DPSDEs have a unique solution and show that the ...
Wei Mao, Liangjian Hu, Xuerong Mao
doaj   +1 more source

Necessary and sufficient condition on global optimality without convexity and second order differentiability

, 2012
The main goal of this paper is to give a necessary and sufficient condition of global optimality for unconstrained optimization problems, when the objective function is not necessarily convex. We use Gâteaux differentiability of the objective function
Burai, Pál
core   +1 more source

The one-sided lipschitz condition in the follow-the-leader approximation of scalar conservation laws

, 2022
We consider the follow-the-leader particle approximation scheme for a 1d scalar conservation law with non-negative compactly supported L∞ initial datum and with a C1 concave flux, which is known to provide convergence towards the entropy solution ρ to ...
Di Francesco, Marco, Stivaletta, Graziano, Francesco, Marco Di   +2 more
core   +1 more source

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

Leader-Following Consensus of One-Sided Lipschitz Multi-Agent Systems with Delay and Stochastic Perturbation

Axioms
This paper is concerned with the leader-following consensus of time-delay multi-agent systems (MASs) with stochastic perturbation over a directed network.
Tuo Zhou
doaj   +1 more source

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

Some Condition for Scalar and Vector Measure Games to Be Lipschitz [PDF]

International Journal of Mathematics and Mathematical Sciences, 2014
We provide a characterization for vector measure gamesν=f∘μinpNA∞, withμvector of nonatomic probability measures, analogous to the one of Tauman for games inpNA, and also provide a necessary and sufficient condition for a particular class of vector measure games to belong toAC∞.
CENTRONE, Francesca, A. Martellotti
openaire   +4 more sources