We introduce a new notion of fuzzy r -interior which is an extension of Chang’s fuzzy interior. Using fuzzy r -interior, we define fuzzy r -semiopen sets and fuzzy r semicontinuous maps which are generalizations of fuzzy semiopen sets and fuzzy semicontinuous maps in Chang’s fuzzy topology, respectively. Some basic properties of fuzzy r -semiopen sets and fuzzy r -semicontinuous maps are invest...

The main concern of this article is to study Ulam stability of the set of ε-approximate minima of a proper lower semicontinuous convex function bounded below on a real normed space X, when the objective function is subjected to small perturbations (in the sense of Attouch & Wets). More precisely, we characterize the class all proper lower semicontinuous convex functions bounded below such that ...

and Applied Analysis 3 Definition 2.1. Let F : K → 2Rn be a set-valued mapping. F is said to be i monotone on K if for each pair of points x, y ∈ K and for all x∗ ∈ F x and y∗ ∈ F y , 〈y∗ − x∗, y − x〉 ≥ 0, ii maximal monotone on K if, for any u ∈ K, 〈ξ − x∗, u − x〉 ≥ 0 for all x ∈ K and all x∗ ∈ F x implies ξ ∈ F u , iii quasimonotone on K if for each pair of points x, y ∈ K and for all x∗ ∈ F ...

We consider a finitely defined game where the payoff for each player at terminal point of is not fixed quantity but varies according to probability distributions on points induced by strategies chosen. prove that if these payoffs have an upper-semicontinuous and convex valued structure then has equilibrium. For this purpose concept myopic equilibrium introduced, generalizes Nash applies games w...

This article concerns robustness analysis for interconnections of two dynamical systems (described by upper semicontinuous differential inclusions) using a generalized notion derivatives associated with locally Lipschitz Lyapunov functions obtained from finite family differentiable functions. We first provide sufficient conditions input-to-state stability inclusions, class nonsmooth (but Lipsch...

We introduce the concept of fuzzy co-r-M -semicontinuous, and investigate the relationships between fuzzy co-r-M -semicontinuous mappings and several types of fuzzy r-minimal semicompactness.

We consider stability with respect to two measures of a difference inclusion, i.e., of a discrete-time dynamical system with the push-forward map being set-valued. We demonstrate that robust stability is equivalent to the existence of a smooth Lyapunov function and that, in fact, a continuous Lyapunov function implies robust stability. We also present a sufficient condition for robust stability...