Elements of quasiconvex subdifferential calculus

A number of rules for the calculus of subdifferentials of generalized conve x functions are displaced. The subdifferentials we use are among the most s ignificant for this class of functions, in particular for quasiconvex funct ions: we treat the Greenberg-Pierskalla's subdifferential and its relatives and the Plastria's lower subdifferential. We also deal with a recently int roduced subdifferential constructed with the help of a generalized derivati ve. We emphasize the case of the sublevel-convolution, an operation analogo us to the infimal convolution, which has proved to be of importance in the field of quasiconvex functions. We provide examples delineating the limits of the rules we provide.