QUASICONVEX FUNCTIONS ON TIME SCALES AND APPLICATIONS

Abstract

In this thesis, the notion of quasiconvex functions on time scales and some properties are established. The subdifferential for quasiconvex function on time scales is presented as well as some properties regarding quasiconvex function. Some Jensen’s inequalities for quasiconvex functions on time scales are also given with some applications. The study again proves that Jensen’s inequality holds for quasiconcave monetary utility function in conjunction with convex, concave, quasiconvex and quasiconcave functions. Jensen’s inequality in addition holds for monetary utility functions with respect to quasiconvex and quasiconcave functions that are linear fractional functions.