and Applied Analysis 3 Lemma 7 (see [15]). LetC be a nonempty closed convex subset of a real Hilbert space H. Let T : C 󳨃→ C be a k-strict pseudo-contractive mapping. Let γ and δ be two nonnegative real numbers such that (γ + δ)k ≤ γ; then 󵄩󵄩󵄩γ (x − y) + δ (Tx − Ty) 󵄩󵄩󵄩 ≤ (γ + δ) 󵄩󵄩󵄩x − y 󵄩󵄩󵄩 , ∀x, y ∈ C. (21) Lemma 8 (see [16]). Let H be a Hilbert space and C a nonempty convex subset of H. Let...

In this paper, first we have established two sets of sufficient conditions for a TS-IF contractive mapping to have unique fixed point in a intuitionistic fuzzy metric space. Then we have defined ( ε , λ ) IF-uniformly locally contractive mapping and η− chainable space, where it has been proved that the ( ε , λ ) IF-uniformly locally contractive mapping possesses a fixed point.

We develop a theory of stratified $LM$-filters which generalizes the theory of stratified $L$-filters. Our stratification condition explicitly depends on a suitable mapping between the lattices $L$ and $M$. If $L$ and $M$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $L$-filters. Based on the stratified $LM$-filters, a general theory of lattice-v...

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 >...

and Applied Analysis 3 In this paper, we firstly present the definition of duality fixed point for a mapping T from E into its dual E∗ as follows. Let E be a Banach space with a single-valued generalized duality mapping Jp : E → E∗. Let T : E → E∗. An element x∗ ∈ E is said to be a generalized duality fixed point of T if Tx∗ Jpx∗. An element x∗ ∈ E is said to be a duality fixed point of T if Tx...