Variational Analysis of Paraconvex Multifunctions

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 properties graphical tangent normal cones between spaces as well sum rule for coderivatives such multifunctions. The use subdifferential lower semicontinuous envelope distance associated multifunction established present paper plays key role study.