The titles published in this series are listed at the end of this volume. 1 1 2 4 4 4 5 5 6 6 7 9 Multifunctions and Derivatives Particular Locally Lipschitz Functions and Related Definitions Generalized Jacobians of Locally Lipschitz Functions Pseudo-Smoothness and D°f Piecewise Functions NCP Functions 1.4 Definitions of Regularity Definitions of Lipschitz Properties Regularity Definitions Fun...

In this paper we introduce and investigate a new type of weaker class namely δ∗-pre-I-continuous and almost δ∗-pre-I-continuous multifunctions in ideal topological space. Some characterizations of almost δ∗ pre-I-continuous multifunctions are obtained. Mathematics Subject Classification: 54C05, 54C08

In this paper, we show how Fitzpatrick functions can be used to obtain various results on the local boundedness, domain and surjectivity of monotone and maximal monotone multifunctions on a Banach space, and also to clarify the relationships between different subclasses of the set of maximal monotone multifunctions.

Using variational analysis techniques, we study subsmooth multifunctions in Banach spaces. In terms of the normal cones and coderivatives, we provide some characterizations for such multifunctions to be calm. Sharper results are obtained for Asplund spaces. We also present some exact formulas of the modulus of the calmness. As applications, we provide some error bound results on nonconvex inequ...

In this paper, we establish some new characterizations of the metric regularity of implicit multifunctions in complete metric spaces by using the lower semicontinuous envelopes of the distance functions for set-valued mappings. Through these new characterizations it is possible to investigate implicit multifunction theorems based on coderivatives and on contingent derivatives as well as the per...

We characterize the local single-valuedness and continuity of multifunctions (set-valued mappings) in terms of their submonotonicity and lower semicontinuity. This result completes the well-known condition that lower semicontinuous, monotone multifunctions are single-valued and continuous. We also show that a multifunction is actually a Lipschitz single-valued mapping if and only if it is submo...

Minimization operators of different strength have been studied in the framework of “predicative (safe) recursion”. In this paper a modification of these operators is presented. By adding the new operator to those used by Bellantoni-Cook and Leivant to characterize the polynomial-time computable functions one obtains a characterization of the nondeterministic polynomial-time computable multifunc...

Jang, Kim and Kwon introduced a multi-valued Choquet integral for multifunctions with respect to real fuzzy measures and Zhang, Guo and Liu established for this kind of integral some convergence theorems. The aim of this paper is to present another type of set-valued Choquet integral, called by us the Aumann-Choquet integral, for non-negative measurable functions with respect to multisubmeasure...