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...

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 ...

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...

The design and performance of a continuous wave dual-frequency multifunction lidar system is presented. The system is based on the use of the nonlinear dynamics of an optically injected semiconductor laser. Under proper operating conditions, the laser emits a dual-frequency beam with a broadly tunable microwave separation. The two optical lines are coherently locked to each other using an exter...

in this paper, a new class of multifunctions, called generalized alpha (mu_{x};mu_{ y} )-continuous multifunctions, has been de ned and studied. some characterizations and severalproperties concerning generalized alpha (mu_{x};mu_{ y} )-continuous multifunctions are obtained. the re-lationships between generalized alpha (mu_{x};mu_{ y} )-continuous multifunctions and some known con-ce...