Our aim in this article is to study the class of so-called $$\rho -$$ paraconvex multifunctions from a Banach space X into subsets another Y. These are defined relation with modulus function :X\rightarrow [0,+\infty )$$ satisfying some suitable conditions. This generalizes $$\gamma >1$$ introduced and studied by Rolewicz, eighties subsequently A. Jourani others authors. We establish regular pro...

The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means linear subspaces, contained in the graphs two (primal and dual) generalized derivatives. This class mappings includes graphically Lipschitzian thus number multifunctions, frequently arising optimization equilibrium problems. developed makes use new derivatives, provides us some calculus rules...

In this note we discuss a special case of the Leray-Schauder alternative for condensing multifunctions.

The aim of this paper is to introduce semi strong na continuous multifunctions and to obtain new results.

In this paper, we study different types of non-additive set multifunctions (such as: uniformly autocontinuous, null-additive, null-null-additive), presenting relationships among them and some of their properties regarding atoms and pseudo-atoms. We also study non-atomicity and non-pseudo-atomicity of regular null-additive set multifunctions defined on the Baire (Borel respectively) δ-ring of a ...

R. Devi, A. Selvakumar and M. Parimala, αψ-closed sets in Topological spaces (Submitted). Y. Kucuk, On some characterizations of δ-continuous multifunctions, Demonstratio Math., Vol 28(3)(1995), 587-595. P. E. Long and L. L. Herrington, The τθ topology and faintly continuous functions, Kyungpook Math. J., 22(1982), 7-14. T. Noiri and V. Popa, Almost weakly continuous multifunctions, Demon-strat...

Metric subregularity (respectively calmness) of multifunctions is a property which is not stable under smooth perturbations, implying that metric subregularity cannot be fully characterized by first order theory. In this paper we derive second order conditions for metric subregularity, both sufficient and necessary, for multifunctions associated with constraint systems as they occur in optimiza...

*Correspondence: [email protected] Department of Mathematics, Binzhou University, Shandong, 256603, P.R. China Abstract The square iterative roots for strictly monotonic and upper semicontinuous functions with one set-valued point were fully described in (Li et al. in Publ. Math. (Debr.) 75:203-220, 2009). As a continuation, we study both strictly monotonic and nonmonotonic multifunctio...