In this paper, we introduce and consider the concept of the prox-regularity of a multifunction. We mainly study the metric subregularity of a generalized equation defined by a proximal closed multifunction between two Hilbert spaces. Using proximal analysis techniques, we provide sufficient and/or necessary conditions for such a generalized equation to have the metric subregularity in Hilbert s...

In this article, we propose a general framework for the study of differential inclusions in Wasserstein space probability measures. Based on earlier geometric insights structure continuity equations, define solutions as absolutely continuous curves whose driving velocity fields are measurable selections multifunction taking their values vector fields. setting, prove three founding results theor...

We consider set-valued mappings deened on a linear normed space with convex closed images in IR n. Our aim is to construct selections which are (Hadamard) directionally diierentiable using some approximation of the mul-tifunction. The constructions suggested assume existence of a cone approximation given by a certain "derivative" of the mapping. The rst one makes use of the properties of Steine...

M by the proliferation of multifunction products, we investigate product portfolio decisions of a single firm by analyzing the impact of three major factors. First, because multifunction products provide complete or partial functionalities of single-function products, we incorporate substitution or cannibalization effects between the potential products. Second, we explicitly model the variable ...

This paper is devoted to the concepts of fuzzy upper and fuzzy lower contra-continuous multifunctions and also some characterizations of them are considered.

We consider set valued mappings de ned on a linear normed space with convex closed images in IRn Our aim is to construct selections which are Hadamard directionally di erentiable using some approximation of the mul tifunction The constructions suggested assume existence of a cone approxima tion given by a certain derivative of the mapping The rst one makes use of the properties of Steiner point...

Let $(X, \tau)$ and $(Y, \sigma)$ be topological spaces in which no separation axioms are assumed, unless explicitly stated if $\mathcal{I}$ is an ideal on $X$.Given a multifunction $F\colon (X, \tau)\rightarrow (Y, \sigma)$, $\alpha,\beta$ operators \tau)$, $\theta,\delta$ proper $X$. We introduce study upper lower $(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuous multifunctions.A said to...

The main aim of this article is to show the role structural stability in financial modelling; that is, a specific “no-arbitrage” property unaffected by small perturbations model’s dynamics. We prove under assumption, given convex compact-valued multifunction, there exists stochastic transition kernel with supports coinciding multifunction and one strong Feller strict sense. also demonstrate pre...