Consider the delay differential equation (1) ẋ(t) = g(x(t), x(t − r)), where r > 0 is a constant and g : 2 → is Lipschitzian. It is shown that if r is small, then the solutions of (1) have the same convergence properties as the solutions of the ordinary differential equation obtained from (1) by ignoring the delay.

In this paper, we consider a new random iteration process to approximate a common random fixed point of a finite family of uniformly quasi-Lipschitzian random mappings in generalized convex metric spaces. Our results presented in this paper extend and improve several recent results. c ©2016 All rights reserved.

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.

– Under general growth assumptions, that include some cases of linear growth, we prove existence of Lipschitzian solutions to the problem of minimizing ∫ b a L(x(s), x ′(s))ds with the boundary conditions x(a)=A, x(b)= B.  2003 Éditions scientifiques et médicales Elsevier SAS MSC: 49N60; 49J65

Abstract: We provide sufficient conditions for radiality and semismoothness. In general Banach spaces, we show that calmness ensures Dini-radiality as well as Dini-convexity of solution set to inequality systems. In finite dimensional spaces, we introduce the concept of Clarke-radiality and semismoothness of orderm and show that each subanalytic set satisfies these properties. Similar propertie...

The purpose of this paper is to study the weak and strong convergence theorems of the implicit iteration process for a countable family of Lipschitzian pseudocontraction mappings in Banach spaces. The results presented in this paper extend and improve some recent results announced by some authors.

Given any finite set of trajectories of a Lipschitzian quantum stochastic differential inclusion (QSDI), there exists a continuous selection from the complex-valued multifunction associated with the solution set of the inclusion, interpolating the matrix elements of the given trajectories. Furthermore, the difference of any two of such solutions is bounded in the seminorm of the locally convex ...