We give a complete characterization of integral functionals which are Lipschitzian on a Lebesgue space Lp with p finite. When the measure is atomless, we characterize the integral functionals which are locally Lipschitzian on such Lebesgue spaces Lp. In every cases, the Lipchitzian properties of the integral functional are described by Lipschitzian properties of the integrand. Mathematics Subje...

We introduce the hybrid method of modified Mann’s iteration for an asymptotically k-strict pseudo-contractive mapping T in the intermediate sense which is necessarily lipschitzian. We establish strong convergence theorem for such method. The result extend and improve the recent ones announced by Inchan and Nammanee, Inchan and concern result of Takahashi, Takeuchi and Kubota [Strong convergence...

Lipschitzian aggregation operators with respect to the natural T indistinguishability operator ET and their powers, and with respect to the residuation → T with respect to a t-norm T and its powers are studied. A t-norm T is proved to be ET -Lipschitzian and → T -Lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an Archimedean t-norm T with additive generator t, t...

We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunctio...

This paper is devoted to study the Lipschitzian/Holderian type global error bound for systems of many finitely convex polynomial inequalities over a polyhedral constraint. Firstly, for systems of this type, we show that under a suitable asymtotic qualification condition, the Lipschitzian type global error bound property is equivalent to the Abadie qualification condition, in particular, the Lip...

In this paper we develop a stability theory for broad classes of parametric generalized equations and variational inequalities in finite dimensions. These objects have a wide range of applications in optimization, nonlinear analysis, mathematical economics, etc. Our main concern is Lipschitzian stability of multivalued solution maps depending on parameters. We employ a new approach of nonsmooth...

The reachable sets of a differential inclusion have nonsmooth topological boundaries in general. The main result of this paper is that under the well–known assumptions of Filippov’s existence theorem (about solutions of differential inclusions), every epi-Lipschitzian initial compact set K ⊂ RN preserves this regularity for a short time, i.e. θF (t, K) is also epi-Lipschitzian for all small t >...

LetK be a closed convex subset of a real Banach space E, T : K → K is continuous pseudocontractive mapping, and f : K → K is a fixed L-Lipschitzian strongly pseudocontractive mapping. For any t ∈ (0,1), let xt be the unique fixed point of t f + (1− t)T . We prove that if T has a fixed point and E has uniformly Gâteaux differentiable norm, such that every nonempty closed bounded convex subset of...