Calmness and Calculus: Two Basic Patterns

Abstract We establish two types of estimates for generalized derivatives set-valued mappings which carry the essence basic patterns observed throughout pile calculus rules. These also illustrate role essential assumptions that accompany these patters, namely calmness on one hand and (fuzzy) inner calmness* other. Afterwards, we study relationship between sufficient conditions various notions (inner) calmness. The aforementioned are applied in order to recover several prominent rules tangents normals as well marginal functions compositions Cartesian products under mild conditions. believe our enhanced approach puts overall into some other light. Some applications findings presented exemplary address necessary optimality minimax optimization problems related recently introduced semismoothness* property.