On the extremal semi-Lipschitz functions

Abstract

The extremal elements of the unit balls of Banach spaces play an important role in the study of the geometry of the space as well as in various applications. For Banach spaces of Lipschitz real functions the extremal elements of the unit ball are investigated in numerous papers (S. Cobzas 1989, J. D. Farmer 1994, N. V. Rao and A. C. Roy 1970, Roy 1968 and in the references therein). In this note we shall present a procedure to obtain extremal elements of the unit ball of the quasi-normed semilinear space of real-valued semi-Lipschitz functions defined on a quasi-metric space.